Google
This is a digital copy of a book that was preserved for generations on Hbrary shelves before it was carefully scanned by Google as part of a project
to make the world's books discoverable online.
It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject
to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books
are our gateways to the past, representing a wealth of history, culture and knowledge that's often difficult to discover.
Marks, notations and other maiginalia present in the original volume will appear in this file - a reminder of this book's long journey from the
publisher to a library and finally to you.
Usage guidelines
Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the
public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing this resource, we liave taken steps to
prevent abuse by commercial parties, including placing technical restrictions on automated querying.
We also ask that you:
+ Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for
personal, non-commercial purposes.
+ Refrain fivm automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine
translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the
use of public domain materials for these purposes and may be able to help.
+ Maintain attributionTht GoogXt "watermark" you see on each file is essential for informing people about this project and helping them find
additional materials through Google Book Search. Please do not remove it.
+ Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Do not assume that just
because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other
countries. Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of
any specific book is allowed. Please do not assume that a book's appearance in Google Book Search means it can be used in any manner
anywhere in the world. Copyright infringement liabili^ can be quite severe.
About Google Book Search
Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers
discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web
at |http : //books . google . com/|
^
/' ^
/
•>^^Vy
!■.«.»*•
..-.•?
:^
»■«»
-^ '*-^
^~J^ C.^.
i!l!(fllfHIIMIflfl!l!IWl
!^Sl^
HiiiiiiiimiMHumiiiiiinnnm
mmmiimuiimuuuuumm
■ >ii>>>tiiiiiiiiiiiiii>iiiiiiii>i(iiiii>i)(iiiiiii(iiin«iitiiiiiiii>iiinMlliiiilRl
•V W"
.*?
Vi
"fV? '
-jT-r-^
• 'J
\-'.
i
.-<*
D-y.
i'
r^
■^-^
c
\:
.-.i
-— ^ -^^
Mathematical Manual ;
CONTAfNING
TABLES
LOGARITHMESi
Numi^ehl Sines, and Tan^etUs,
WITH
The manifold life thereof briefly
Eicplained and Applied in Arithmetick^^
Geometry^ Afironomy^ Q^ogra^hy^
Smveying , Navigation , Dialling ,
Gnnneryy and Gauging,
^HENRT PHILLlPPES.
-. 5 ft — : — _
tONDOK. -
Printed by A. C lor i^ for W.Fifhefy i. thomas-,
jMrthcoty and E. Hurlickznd are to be fold at the
^ofttrngaU nav Torjier^Uly at the Jdam and
Eve in Little Bntain^ at the j4nchor and
J^arriner near London-Bridg^ and atthe
Rofe at the W[/?-w4of St.T/ruls. 1577^
- V
V
J
r
V*:
• • •
5,^' To the Right Honourable
Sir Wittiam Turner Kt.
Lord Mayor of the City
O F
LONDON-
Right Honourable, and ay
very good Lord,
'g beuttd Jtfttayffur
ordjhif ina- ebublo
] TTtd , not only as A
rkfote Citi%en^ but
' a Public^ (Micet
' 'Jer yoitr Cogni-
\ my Duty ^ not on-
ly with the general Viice and Plaudit
of the City , but in fome mere fublic^
way J to render to yoitr Lordfiip
taqji .humble and hearty Thanks for
your ajjiduate and indefatigable in-
dkfiry^ which, hy the Blejjing of Al-
tnightyGod, hath in fo great andun-
expeHed meajkre net only refiored owe
A 3 Rjfinoits
The Epiftlc Dedicatory.
Ruinous City to its former Condition^
but^hatb rdifid it to a far ^ore excel-
lent Glcrj and Beauty than ever it had^
or was liks to have^ before. As we
fnuji all acknowledge^ That our Merci"
ful God bath principally and primarily
broHjM ff^^^ Ooodout ofEivil^ fo we
muft alfo c^infefs^ That your Lordfiip's-
lionour hath been herein a prudent ]o^
leph under our Royal Soz>ereign^ and a
diligent . Nehemiafi in the repairing of
our Hierufalera 5 and^ That the Wor\
hath exceedingly profpered . in yout
hands.
. And novp^ myjjord^ though I want
Means and SJ^l/ to further fo good aWark^
as I would ^yet I want not a Mind to do
what lean : And therefore I have been
( perhaps fomewhat too') forward to
pfiblijh This 5 and fome other Books of
this nature. But if your Honour will
pleaje to caji, a favourable Eye npon it\y
I doubt not but tkts little Mannal will
be of great ufe'to all Mathematical
Artificers employed* in Building and
BeaHtifyifig the City 5 a^d Hkewije to
all
I
1
TheEpiftle Dcdicatory.-
aU Navigators and Sedmcft^ vph§ are
entrufled tpith the Shipping and Mer-
chandize thereof^ vphtrein the chief
Riches^ Strength^ and Glor/^ notomy
of the City^ hut of the iphde Kingdom
doth conml.
The Advancement vphereof dsit is
your Lordjhips prejent Care^fo^ it Jkall
be my daily and earneji Prayer , That
God would continue to bkfs your La^
hours herein 5 and^ That you may live
to fee this Work^hronght toperfeSion^
to the Honour of your Lordfiip^ the Glo^
ry of the City^ the (!ron>n and Dignity
of our Gracious Sovereign^ and the Wei--
fare of the' whole Kingdom. So cra^
wng your Lordjhips pardon for my
holdnejSy I rejt^
YourHbnotirs moft humble
Servant «nd Officer,
HENRr FHlLLirPES.
A 3
r
CO
* 1 , .
^i^— Il ' ' ' ■ ' '
THE
EXP Lie ATIO N
Of the following
Tables of Logarithmes^
|N this little Book, which I intend
only for a Manual or Pocket-Book,
I fliall not trouble you with the
tnanncr of, G)n{lrudioii of thefe
Tables of Logarithmes > but ftall only firft
give you fome brief general Rwles for the bet*
tcr underftanding ol the Tables,and the man-
ner of u(ing them) and then give you fome
ufeful and necefTary Propofitions in Arith-
metick, Geometry, Aftronomy, Geography,
NavTgation,DiaIling,Gauging,and other Ma-
thematical Arts, which may be of daily ufe,
and are moft eaGly performed by thefe Tables.
^ C# H. /\ Jr • !•
/
To find the Logariphme of unj I^tmier
md^r ICO.
1^ Begin with the Table of Logarithmes fof
Numbers, though kft placed » and the
nature of thefe Logarithme Numbers is fuch,
that let the Number be never fo fmall, or
A 4 great.
2 Tbe txfltcaUon of
great, yet the"Logarithmc mull have the like
nuraher of Places or Figuies: Now folBc
make them to ii Places or Figures, as
Mr. ^ggs \ Tonie to eight PIaces,as Mr. Gwt-.
ter and Mr* Kdrttfood v and fomc to 7 Places, as
Mr. JFingatezx\i}At.Wing v and according-
ly! have fitted thefe Tables to 7 Places: And
in the fifft Pageof the Table you (hall find
every Logarithme plaiply let down to its pro-
per Number, from one to an hundred, after
this manner. . >
Jbi Logarithme of, lU o, ooocJCo;
'the' Logarithme of 2 is 0,301030
The Logarithme of 10 w i, ocooob.
The Logarithme of 2ois 1,301630
And Jh for aU the reft to 100.
T[be Logarithme rpber^cfif 2,ooooop.
Now in thele Logarithme t^urabers you
muft take itotice that each Logarithme is di-
vided into two parts \ the one is the Chara^^
deriAical Figure, which ^ is the fir (I Figure
, thereof, arid only (hews of how many^ Fi-
gures or Places.^hel»?utpbcr iignified thereby,
doth confift : 'the 'other ' lix Figures (hew
more exaAiy the jafi Number iignified by.t})$
Logarithme. ,^.: i •,:,..%
Thus all Numberafrom i to-id have for
their Charadieriftica Cyp1ier,thuSiO,bpQOOO'^
and all N timbers from id to 100 have for
their Charadlerittick a Figure of one, thus^
' ' ' * 1,000000 i
theTables of Logarithmes. ^ 5
1,000000^ and all Numbers from 100 to
1000 have for their CharaAeriftick a Figure
of 2) thus, 2)Ooooco s and all Numbers (rom
looo to*i 0000 a Figure of 3 ,thus,3 ,oooooo»
and all ffom loboo to 1 00000 have for their
• • • ^ "*
Charaderiftick a Figure of 4^thas 4>cooooo»
And fo if you proceed further, the CharaiSe-
riftical f ij^lire is always one lefs* thad the
Places or Figures of the Nuix^er*
Chap, il ~"'
To find the Logarithme of any Number
from 100 to 1000.
ALL Numbers from 100 to 1000 arc fet
dowo focceffively in the Table follow-
ing in the Margin of thefeveral Leaves, and
their Logaifithmes are fct. down in the ntXt
Colurhn juft^y thefn,which Column is mark-
ed at the top thus [^ cr] \ only ^ou inuft put
their ChaTaderiBical Figure, which isa, be-
fore them, as I (hewed before. Thu.«,
.^ * 'the hogaritbrnt^ 1 00 is 2 ,000000
T^fe^ Logaritbme of lOi is 2 ,0043 2 1
Tbi L(^aritbmt of 102 is 2,oo8doo
~ « ' Tie Logaritbmt if no is 2,04 1 3P5
'the Logarithnte of 120 is 2 ,07^ 181
- And fo for any Number to 1000 fucccf-
Cvely in this hrft Column to the end of ihc
Tablf.
CHAP.
JJie^Explicati'm of
CHAP. III.
r^ Jmd the Logarithm of any Number
from looo to looob*
HEfe yen iiiufi.obferye, That the Table is
divided ioto lo large Columns^ five
on the one (ide of the Book, and five on the
other ) alio eicb of tht Numbers in the Mar-
gin are Cuppofedtobeincrcafed by lO) and
tnc;Figurc$ b i 25456 78 p, which arc
fet at the head of each Golunnn, are to be put
to th^ Figures in the Margin^ to make them a
place more, and (b are co be rca4 after this
oEUoner*
190 lOOO loot 1002 1003 1005
And (b the Logarichmes of thole Numbers
fland in the fevcral Golttcons under them s
only joa muft prefix the Chara<Seriflical Fi«
gure of } befof e them. Thus,
T[be Logd^rkbrne of lOOO 1/3, 000000
'tbt LpgariHfme of lOO i k 3,00043 4
Zbe Juog^rithmi of 1 002 it 3 , oooStf ?
And (q read along that Lineto loio, for
which you muO comeback agatn to the Mar*
gin of the next Line, and there the Number ^
IS ^
tk Tables of Logarithmes. 5
isioi, to which adding the Cypher or Fi^
gures at the top of the Columns, they wtU
nake ipio, loii, 1012, ioi3,<^c. to loto^
and their Logarithmes arc in the next Line^
VIS*
lOIO
lOII
loia
1P13
10J4
3,004321 I
3,004751 I
3)005180
3,ootfo3S
1 01 5 $^006^66
loiy 3,007321
1 01 8 3,007748
^^^9 3j<»8i74
And thus you niay find the Lc^arithme of
any Number under 1 0000 plainly expisflcid
in this Table, which after a little uft wiH tic
as familiar, as if each Number were )oya^4
to its Logaciihme, as they are in the larger
Tables of Mr. Brigi^ Ms. Gellihand^ Ncar^
wmdy&e* ,
mmmm^f^
C H A P. IV-
Tofndthe Logarithm^ of anj Nmnhci^
from loooo U looooa
As before the Marginal Numbers vHXt
divided into 10 parts, fo now you
nuft fuppofc each of thefie in the fcreralCo^
iumns to be divided into 10 parts, and for
the better perfbmucig of this> the Difftfcn-
ces
6 TheUxpUcAtion of
ces between the Logarithmes in each Column
are fct down in the Margin on the right
hand \ which iJiiTerence being divided in-
to ;[o equal parts, will make the proporti-
onal Logarithraes for the Intermedial Nam^
bcrs, to whifh you mqft prefix the proper
Charadleriftid{, which is 4 *» fp have ymi the
Logarithnie tonnplcat.
^ Tbms iht Log* if J 000 Mng 3 , cooooo
And the Le^. tf 1 001 bdng 3 , 00043 4
l^hc difference betwHH them is 434
wbi^bheiKg divided inu 10 equ^lfdrts, wiB
MMJ^f the Logariihmes of thfi iHUrmdial
NMmberijo fptaeej^ ihiu.
jocoo 4,000000
1 0001 4,000643
I0P02 4^000087
10003 4,000130
tt9eo4 4,000174
I
10005
1000^
J 0007
lOOoS
lOOOp'
4,coo2 17
4,0002 do
4,000304
4,000347
4,0003^0
But in Hnding out apy of thf fe iiiterme-
dial Logarithnrfts, youinted inot wrife them
ovir all> but multiply Uic Difference by yovut
Sotcrmedial Number* - ^
Tbus if ym ~$Poktd findtbe Logsiitbme of
10005; The Vifereneebttftg^^/^ fnuUiply
this by 5, it mak^ at 70*, jhen cHt^g fff
the Idji figttrty is mil be 2I7> tpbich' added
i0 the Logaritbme <f loooo, makis 4^0002 1 7,
asbefvre.
To help Ijerei^n^ there is a Prqpottional
tabk
Tbe'Tablct oj Lcgarjthmes. y
Tabic at the end h^reoC, were each Num-
ber to be added to the foregoing Logarithme
is ready caft up to your hand. The thing
is fo plain, that it needs no Exatpple, bat
^hatis before faid:. Only the Tabic makes
the Work more ready for you.
CHAP. V.
A Logarithme being given^, to find attt
the Number belonging thereunto.
THis is but the converte of the former^and
therefore you muft remen^ber your for-
mer Rules, concerning the CharaderiAial
Figure ^ which,' if it be the Figure of i, tfien
yourNwmber is to be under lOOi if it be
the Figitire i, then, your Number defired
muft be under iooO) if it be the Figure j,
then your Number muft be under icooo >
if 4) then the Numberis under looooo.
Look therefore in the Tables till youfiad
the Logarithme given, and ag^inftitin tbe
Margin, according to the former Rules, you
(hall fee tbe Nuthber belonging thereunto.
^1^2,07^ 1 8 1 Care the 1^4- J 120
}3 >07P 1 8 1 r ritbmes cf S 1 2 00
4,079181 J r 12000
If
9 The Explica$imcf
If you cannot find the Logaritfatn gi?eii
c^adly in the Tables ( in mofi Operations )
you may take the nearefl Logarithit) Nucnber
which you can find^ cither greater orlcfs,
and take the Number belonging thereunto for
^our Number deiited.
y
CHAP. VI.
/
\
To find € Logarithme bebftging to a fra*^
3ion^ or a Mixt Number ^ confifiing
of an whole Number and a Fta^ion.
DEduA the Logarithme of the Numcra*
tor out of the Logarithme of the Dc-
liomioator, the Retnainer is the Logarithme
of the Fradion propounded*
Thus if yoH vpould find the Logaritbme of
4, ihe Lcgariibme rf 4 U—hog*^* o,tfo2Ptf o
And the Lpgaritbme ef ^is-hog* 3» 0.47712 r
iFbkb fiAtraStdteavti Rf#i-o, 124939
for the Logarithme of \. ' ^
But thebefi way in thefe Operations is to
turn your FraiSion or mixt Number into a
Decimal Fra6Jion: So the Work will be far
more eafie, efpecially in mixed Numbers.
For Example, Ltt the Logarithmcs tf thefi
Numbiri be required 12, 12^, I2ijiaj;, you
the labiesoj LogArithmes 9
mcy readily turn thefe into Decimal Nnmhers^
fo they mil be I2, 12 ("25, 12(50, 12(75.
Notif to find the Logarithmes for tbefe Num^
bersy lool^for them as if they were whole Num-*
berSy only hgef th^ famt CharaSerifticI^ which
beloHgttothe whole Knmber 12, which is u
TthmfoT
12 %. I,c7pi8t
1225 /li* i,oSSi3tf
^1275/^^.1, I055IO
« Bat here by the way you may cake notice,
That though it be eafie to reduce thefe ordi-
nary Frldions of Qiiarcers and ff alfs into
Dccinnals, yet in other FtaSlions it is not fo
eafie, but you mu(}.workby this Rule. '
Addturoof three Figures to your Nume*
rator> and then divide it by your Denomi-
nator 9 fo you (hall find a £)eciinal Number
cxadly equal to your Fradion : Or el(e, by
adding of more Cyphers, and continuing
your divifios^you may make it anfwer there**
unto.without any confiderable difference.
•3 1 (0^25
^ § M125
t V« 2 ^o, i66i
2^4^^ ^ (0,0417
•;;\j ^o,tf 2 5
-.-^^^1 WI2S -., . ^ ,
And having thus found the Decimal
Number anlWering to the Fradion; you may
add it to the end of your whole Numbery
and
10 , Jibe t^pljcation of
and (b find out the Logaiithme thereof by
the former Rules.
>
CHAP. VII.
The Logarithme of a mixt Number be-'
ing given ^ to find the Number an-
fiperable thereunto.
THis Problem, though it be but the con-
▼erfeof the other, yet it will feirvc yc-
jry well to explain moft that hath- been faid
i>efore, efpccially that concerning Decimal
Fractions, which is very ufeful.
For Example, Lef the Logaritbtke given he
l)0SSi3', and it ij required tofindtheNum^
her eorreffondent thirmnto.
In the firfi place obferve, that theChara^^
deriftickis I i therefore the Number fignift-
cd thereby is more than lo, and lefs than
loo, therefore I look for this Logarithme ia
the firft Page of the Table oi Logarithmcs ,
arid find that the nearcft Number thereunto
]Si)07pi8i, which is the Logarithme of
12. So that ^he natural Number exprcfied
hereby is fomewhat more than 12, and yet
Ie(s than 13 by above one half*. And tVus iTl
Logarithmcs that cannot bcfound exa^ly ex-
prcficd
the Tables of Logarifhmes. il
preflcd in the Tables, are mixed Numbers,
aiid to be exprcficd by a Decimal Frai^ton.
Secondly, To knqw hp.w iDuch it is more
than i2more^xadly, go to the foIlo)|?itig
Tablc) V9\i^th {hcHf^ the,Logariiltme%dC all
{lumbers fromioo, to loooo, and there I
find for the Log. of 1220 or I2(20^n^itting
the Gharadcrifiick ^oti^^py and fdr the
Log. of 1236 or 12 (|©, oSp9q< : Sp^tha(;
it kerns to be much^ in the middle way be*
tween tUc(c two Nutnbers, , , v.
Thirdly , Therefore tunning along the
Line againft 122) in the firft Column' pn the
right*hand-(ide, whidi hath the Figure j( at,
thetep, I find my forctaid Log.. 688131^
exad!yi andthcr^orc I conclude, that thfi
Nunabtt expreiTcd thereby is exad:ly 12(2.$^
' LaAly, If you c«ufd not hayefound.tbis
XogarithYne here exadfly, then it mu(j^faft
between this Number aiid the ncxt.m tl^
fanne Line, that is. between 122s ^"4 t22tf «
and by the Psflference, and the Table ^f Pre-
portion, you ofay foon fitid hoW dtiuch it i$
more. .",-.,.•-'
/> Asfuppofethe Log. had {)ecn 0^1^314,
this fs more than the aforefaid Log.^ 08S130
by 178, which is th^ half of tlic commop
Difkttnct kt at the end ctf* this Llne^ bpng
95 5 f and fo the Naoabet defired is 12(2 5 5«
i CHA?.
12, The hxflMtMttef.
fi
. rii . c H A p. vm.
(I *
^/ ihe Vfe of the tabk of Proforthk:
J i
f}cn you have the difference between
. Uny i9f& Logaiithmcs ^ you muft
iihi'ounheProportrdnalPaftof th»t diffe-
rehc6l?thtr'by the Riile of Propoition, oi
fey the Table of Proportion, which is fitted
wjt tifii^urpofe. * / ,
rnj ^ the Rule hatKtwo Cafes, ...
l^ fii^y-Kn§mHg the Commn di^triHie, ti
ftM^a^hat yoii mHJiadd fjo/r any itfi^rmdiAU
iJiidhw. This ia pciforntted by M^il^plica-
* ^' 3^1010355: Se^tp 10^(5.
And fo/or any; qthfr of. the ip iQtciiflQediati^
-^ i -The Second tafe is, KM»rmg ^e , CfW»«
T9Pf%rWcr» ^and likfmje the FartkuUr J^ffe-
^ortrV bf yoHT Hunger yfrwi iht jL«f. fom^d
Uibe^aik. TFiis isperfoiracd by Divifion^
aftcir
the Tables of Logarithms. t g
after this manhcr. Let the Common diflfe-
xencebe055, and your particular Diffi:rence
143, or 177(5*
4s 355 to to: So' 14.2 to 4.
-^/355 *tf ro: 5'<^i7y(5fa 5.
As^^^ toioi S9 2%fta6.
And fo for any other of the jointernbediiMe
Numbers.
But now the Proportional Numbers are
^eady cafi up in the Talilet of Proportion i
fothatbytheCoimmon Dlflference ypa may
in that Line And. all the ten Numbers ^hidl
you tittA to ufe in boih Caies, without aify
farther trouble. * . ^
Example. Let the Cbmmon plfferen ee te
355) as befpre > the Proportional Nnmbers
are thus fet down,
1234 s ^ i^^ 9
355^35:^i.io<5i4^)i77,2i3»248,a84,3i#
which you may ufe according to fetmcr dire*
^ions) aRcl fo this (hort Conipendium of
1 0000 Log. will make 1 00000, which will
be aa^far as is ufeful in moii Cafes. If you
will make them to fer ve for a Kf iltion, yqu
tnay do it by working the Rule of Three to
a place further. Thus, .
AsiQOtoi^^i S9iioi[%%.
if/ 10010355: S02toj(i. •
As ioO 1^355: So 3 to 10(^5.
14 The ExpIicatiffH bf
And fo in the ethex Ca(e«
1^/3551^100: 50 14' 2,^04*
J/ 355 #0100: 5017(751*05-
if/ 355 10 100: 50aii,3,i0^.
Thisalfo ouy be perfoimea by the Tablet
of I^iopprtioOy counting. the dnglc Numbers
It ^9 3#c.to iiand hR for 10, > a 30, and
then cutting off the laft Figure of the Pro^
portional Nambers, the reft will ierve for the
ringkD]^ts4)a,3» &c. *
^iit this being in mofi Cafes needfeG, and
ia^fo the Logaritbme Differences being fcaice
exad enough to ferye to 100 places, Khali
not inGftuponit, but rather, advice you to
yfe a brgec Table of Log^rithofies^
I
• •
tnt.
<• I
I
5
EXPLICATION?
OF THE
Tables ef Sines and Tat^ents,
CHAP. IX.
I
t '
Any Arfipr 4^gl^ofa Triangle^ cm-
paining any nwnher of Degrees and
Minut^ being given , to find the
Logaritl^me of the Right Sjpe or Tan^
^ent belonging thereunto.
FIrft, Yoa pnft iindcrftand, iFhat ever]r
Circle is diyidcd intofouir Quadrants^,
pr QinirteTS ) and each Quadrant is diiride4
IniQ fo D^ees, and each* Degree into do
lilinutes^and the Logarithme Sines and Tanr
gents fer every one of tbefe Degrees aad Mi-*
sutes are plainly expireffed in thefe Tables,
and ate thus ro be fonpd*
When the Nun^>etof the Degrees. given
B 3 doth
1 6 The Explication of
doth not exceed 45 dag. make fearch for the
. fiine at the top of The Pages of the TM§m-
kituled Artificial Sims smd "tangents > and
if there be any Minutes joined to the Degrees,
yoB tnoft find tkeni out in the fiifi Column
or Margin to\^ardi the left hand, which is
marked with the Letter M : And having fo
done, right againft thofe Minutes, under the
Title 5igii, at the top of the Table, you (ball
iindtheLog. 6f the £ud Sineai}dM||pbcei
and under the Title tangent you (hall have
the Log. of the Tsingcnt of the Ark or Angle
de(ired.
So the Log* of the Sine of an Angle of 2 ^
sL^o m* is 9,^oj€0 > AndtbeLog^ of the
\tangent(f the 'fame Angle is p^^383©l.
But when tiia Number of the Dcg. trqui-
led exceeds 45^ you itiuft look ib^iihem at
tbebottomof thefaid Tabk, and^youmuft
look for the odd Mtputesin the ftlftCt^lucon
or Margin towards the right hand, marlced
lihewife with the MtterM^ and fo Mght
agaiuft thefe A4inute% in the Column above
tlx; Title Sine^ 'you fliall find the Lqg. of the
faSd Sine s and above, the Title lanjgeni^^ y ou
(ball find * the Log.of the faid TangcQt of the
Anji^e required* . ■ , . . , ; .
< «V<r ittljig. Sw of 66 dag.,xomin. is
9^962^9^ \ and the Lag^ofjhe.JaMg^ist of
the faj^A^gltiit ho^n i4l6pdi^* ^^d thus
•'• i* .; you
the Tables rf Sines 4nd Tangents, f 7
yeumay licul the Logarithtne Sine or Tan*
§em of any other Angle* -
> . » ... .. ' ... . T . , , ' t u ti^
CHAP. X. \
To find the Confine «rC<H4ngf/ff */ ^*ff
THe Co-fine or Ovtangenc of any Angle,
is that which others call the Comple*
ment of any Angle, ortnore planely, the ttt
maining pare of that Angle being taken ont
of ^o Degr^s. tbuftbe j^ngUrf 2^ deg.
^Onnn* being uhf^ out if 90 deg* tbiComfU-
ment thereof^ ml! be fmnd to be 66 deg. ^om*
And on the other {ide, 'the Anglo of 64 deg.
^omw* hnHgtakfH ou^ cf fo deg* gives f^
fbe ComPlemeni tbereof 23 deg* $0 min* So
that thele two Angles are (he Compleipents
of each other : And (0 you (hall find the
Complements of any other Angles. ;'
Now thefe Complem^ts being of freqaent
uic in Trigonometry, it hath been ^e care of
mofi modern Mathematicians fo to compofe
their Tables of Sines and Tangents^that thefe
Complements (hould be aly^ays joyned or
coupled together ; And therefore M^. Gnnter
very fitly calls them Co-fines and Co-tan-
,84 gcnt$
1 3 , Thebxplicmm^
gcn^. 4n<) this is dpne by maHiog (he T>7
bles of Sints and Tangents ( an4 Secants;
where tl^ere is any) to run on frooi odtg. to
4$ ^« with cheit refpeAive Titles at (he top
ot the Table 9 and then from 45 tUg. to po
i/ig. they turn back again in ordcr^ with their
fcfpcdivc Titles at the botjonn of the Table*
^hus tlie Si'n? and Tangent of dvefy Degset
and Minute in one Oolansn, is joyned with
its Sine-Compltnnent and Tangent- Comple-
ment In the next Column* So that without
the trouble pf fubtra^iog the Angle fro^i
$Q deg. you may readily find thcComple^
ment thereof, t/ifi« either, the Arch or Angle
jn Degrees or Minutes, or the Log. Sine or
Tat^cnt by tht Arch, accordifsg as you hav^
occafion.' \ .^ > /
7tms the ComfUnuntof the A^gU 23 dig.
3<\w». i/ 46 dig* iomift. ihtlJga' Sine
t^bhtof in 9',f62^f%^ nndtht Log* Tangent
theresfif lo.^tf itfpt.
So liketifije the ComfUment 9/^ the Angle
66 deg. 30 min. biing 2) dig. 30 mitf. the
Ltf^^Sine thereof is 9^600^00^ and the Log*
T^angent 9)^38302*' And fofor any other
Angle, the Co-line is fttll coupled with it 11^
the ad joyning Column.
r I
CHAP,
^^^TabksrfSmsandTaffgeftts. 19
CHAP. XL
Tpfnd the- ^eca^t of any AngU, and
m Artthmetical Complements inflead^
thfreofi , J y
T"xf2?'"'? -Wsare vciynccdSiy in
A TaWes, fo? the txpcdWug o£^alcal«-
tioq i and likc^ife the Logaritfc<toc Sccamt
(pr at kafl a patt of them ; ar/cf goodufe,
as I flwll Aew heieaftcjc /And therefore
though m this little Bookwchadnot room
to fct them dovm, yctlftallOicw you how
you nay eafily find ifetm out by the Table
of Sines. ,
the.Jia^'
ComplciBcnt of any Angle firoro the double
Radius of the Tables, and that which re-
mains wiH be the Secant required. At if I
d^re the Stemt ^ 23 dtg. 30 mm. / findtbt
Log. Sine of its Comptmtnt is 996230% .
f^wb fHbtraaed from the doubh of the Ra-
duut thai is, 20,ooooco, tbere remeint
10,037*02, which is the StcMt of 23 deg.
30 mtH. Andfi alfa, ^ 0.^9 9 30^ is' the
Stcant of 66 dtg. ^omiu. it being tht remain-
ttef f 5*00700 ti^H oHt of 2 o, 000000. '
Noir
/
' *
ao The Bxplicdtim ef
Kow though thefc Secants be of Hitle ufir,
yet the latter pare thereof, leaving oujt the
* Charaderiflick, is of great ufe, as you (hall
fee by and by. And therefore it will not be
amtfs to (hew you how to find out thefe
Arithmetical Complements, that is, to fub*
'^A any logarithm ' Number out of the
dromon Radius, which is io,oooo60, af-
ter ihe moft ready way.
' FotEzample, Jfy9u wen to fuhirgQ the
fanfdi tdgarithme Sine 9,962^9% eut of
iktltjtdius\c ^000000: 'the tommm way is
fifft tojetdimt the Radius — ■ io»oooooo
m^\
2fcf» to fitbtraa the one from7 o, 037jfioa
the other ^ fi the Kemdner is- y *
But to ifubtrad the Complement of this,
or any other Number more readily, you ruay
begin (contrary to the common courfe)with
the firfi Figure towards the left hand, and
write down the ^Complement or Remainer
thereof to 9 > and fo do alfo with the all reft
of fht Figures, faying, 9 wants ^
00^ p, and again, ^.wants, o,«^'J JJ
wants 3. 3 wants 7, 3 wants * ^^
d, 9 wants o > only when you come to the
lafl Figure, take it out of 10 j fo 8 wants 2
ci 10 ; butxCQUnt upon 9 for all the former*
Thus you may readily write out the Arith-
metical
the Tables rf Sines and Tangents. 1 1
tnetical Complement of any Sine out of the
Tabic, .aloiofi as eaOeas the Sine it felf ) and
therefore in this little Book I have the rather
omitted, theo).
In the like manner, if ypu need the Arith-
metical Complement of any Log. Number,
you may thus readily fubtradft it* But if^'
you need the Arithmetical Comp!ement^/<a
any Tangent, you may take theCO'taMK^it ,
which is the exa& ArichmetkajlCompftment
of the double Radius 9 fo that thrTangcat
and Cp-tangent of any Arch np^Ke cxadly
20,000000. BytWs alio yo/may try the
truth of the Tables for the Tangents, and
correal (hem if need be.
CHAP. XII.
To find ant the Natural Sine or Tangent
, of any AngU.
m
IF you want a Table of Natural Sines and
Tangents, and dcfire to know the Natu-
falSineor Tangent of any Angle, lookout
the Logarithme Sine or Tangent in thcfe Ta-
bles : Then not much regarding theChara*
fteriftick thereof, fee what Numbdr wHl an-
fwcr to thcothcr part thereof in the Table of
JLogarithrac
2? T^e ExpMcsfim of
Logari^hme Numbers!^ and that With a tttt}^
caution will (hew yba the Natural Sine or
Tangent i]€(irecl.
Exannple, Jdefhre fo l^ow the Natural Sine
if 2^d. 30 nun. Firfil jiffd ibl Log* Sine
f hereof in theft tables j and it U 9, tf 00700.
Tketi (nnltiing the Chara&eriJUt^p^ I fi^K
for fed jog m fke talfU of Log. Nuti^ers^
fffd ^ Heartjt Log^ Htiif4^ J can find there
is 6oo^ifi^ nud the Natural ifumher Unjmer^
ittg tberetthto is 3P^7) ift^hicb is the Natural
Sine of the faid An^e , if you content your
felf mth a Radius of 10000 \but if you m^
your Radius i6o;)ob) then the Sikefiimldbe
59875- /
And fo by Proportion and the former
Kules, if your Tables were large enough, you
might find any Shie or Tangent to a Radius
of 7 or S FiguresvAs by the Chara^ertliicks of
the Log.Sines youaiay (^e they arc made to i'
Radius of 11 Figuri^s or I^lace^, the Chara*
derifijck of their Radius being 10,000000,
K^ich (hews their Natural Radius is
10)000)000,000, though there be but 3
figures or Places in the Log. Radius, t he reii
being oautted, thefe being taken out of farger
Tables, and ytt will {erye nry well m3 cnof^
ordinary Coocluiions.
THE
33
• *
tHE
SECOND PARti
S H E W I N G
The Ufe <^ thcfe Tables of L(h
ggrithms in leveral Parts of the
MATHEM ATICKS.
In Afithmetick^
PfopofitioD J.
Ho fMhiftj (fne Number ty'M0ibin
LOok tte Lbgatkhth^f each Number iik
the Table of Logarithm Nambers^ ac«
cordliDg to tbcfbrmer Rules, and wiite them
down one under the other, and then add the
two Log. together by the common Rules of
Arithmeticki fo they will produce a third
Logarithme, which third Log- being found
tint in the Table of Log. you may thereby
6ni out' the true Number, which wodld te
^rodutedf by the nultipKcation of thefeid
Example
24 Arithmetical Propofitioffs:^
Example, ^obrnggi^m to be mtMflied
7btLog. rf^o being — ^1^^7712 j
JdJtd to tbi Leg* rf^j "^^3P7y 4Q
Afal^fsaibird Log^' — ^ * — ~"2vS75otfr
spbicb according to tbi former Hules ym mil
find t9 he the Log. of 75c, v^b is Hbe trr
dtiSof tbtmHliifHcation*
Now tKc Rcafon of this dperation is
fetoundcd upori the Rale of Proportion ^
which fs itnpHcitly required in every Mdlci^
plicatior). ^ So that, '
Jiihtoio: ^Sois z$to'j^o.
ThatiS) So many times as i is in ^Oj fo ma^
ny times 2 5 is contained inj 50.
, Now becaufe a Unit, whith i$ the firft
Numbeji^) doth neither multiply nor divide ^
therefotjC the Tables are fo framed, that the
Logarithtfi of i is p^OQoooo, only Cyphers,
which do neither add nor (uUiaA^ and Ri
inay fee U(t out» and yet the Log. of the other
t WD Numbers, being added together^ fully
txprefithe ProduA which is;ide(iccd.
Tiielike cifeft will foUow if you u^e Dc-
titmA Fusions in mixt Numbers.
, Example* If jo mit tobe mulnptiedby 2/$.
JT&e Log. cfio ir-~- — • 1,4771 ti
T^beLog. rf z(i is 'J^^}979^o
iyhicb maketb^ '• — ^ 1587^0* t
tphicb is tbi Log. (^ T%.
a Bbt
Ariihmetical Pnfopions. 3$
But if the Numbeis |ou are to maltiplj^
by, be either one or both of them pure Fra-
dions, that is, lefs tha'ft one Integer of your
Mnltiplieation, you muft be careful how to
chaiaaerizt your defedive Lagarithtn, and
to place yoHr Produft accordingly*
Yoii muft here underfland^ That the Cha«
Jraderifiick of iiso,ocoooov therefo|re the
Charaderift'ick of a Fradion thit is always
lefs than t, cpuft be lefs than o^ooooob;
And in the fame tnanaet astheCharadcii*
iRicks of whole Numbers increafe to be more
than o,oooooO| fothe CiiaraderiAicks oC
Fradions decrease kfs.than 0,000066, and
are to be marked with a Note of defed thus ^
— ,as you may fee by the Logarithms of
theft Numbers and Fradibns. ■' ,
Nnnib. Logaritbm.
5000 ^769^9 JO
5.obo o^6^%9'j6
0*050 ^*i,^:^Jp7o
0.005 ''2^69%9jo
Ntew* the beft way -to nnderftand ypuf
jProdujjS is by obfcrving thefe Examples >
wherein I have explained the Opcratipn, by
ftialtiplying thcfc Decimal^ Fradions in si
Natural way, filling up all the Places with
Cyphers, which makes ic very plain.
Example i.
a 6 Jrithmeticdl Propojitions.
Example i. Multiply 5 ^y s*
I ~ •
.M-... tog. 25 i,397?4o
Example a. Multiply ^by 0, 5 i . lib^f J i/>
iy jSw tr«if» parts^ or an half.
,0 Log. 5,0 o,dp8j^70
,J , tog. Q,5 — o.tfpSyyo
ijjo i^^. 2,$ — i>ip7>4^
00
— i'hisis the Logarithm of 2 5
2,^0 as before: But here being onq
of the Numbers AtkGtvtty it
(fiews (he figures are to be fetaplace for-
i^ardfer, JisFradions^ (o there remains for
theProdud 2)5) or 2, 50 parts 9 that is, tWo
Integers iad an half.
Eximpk i^ Mmhiflyo^^byd^^.
0>5 I^* 0,5- — 6,^^^970
<2>jy -E«g» OjS •-'6^<5#8y7d
• " ■l"*^-
25 I^|;4 i 5 — 15397P40
00
— . JThis • is. tlie Logarithtn -of
0,2 5 2$ ftill *> but beeaufc aft the
t^ umbers ire <jlefedtiTe,it^ft^^^ '
ibis o^ 5 mulil be f<;t two places fprwara^and
made all Fra^ions : ^othe Produd will be
/
Arithmetical Profoftians. 2 7
6, 2 5 hundred parts, chat is^ a quarter of one
Integer. ^
Here you nnay farther take notice, that In*
tcgers, mukiplicd by Integers, produce Inte-
gc;i9, as in the tirft Examp^ic : a^d Integers^
multiplied by parts,produce loteg. amd Parts,
as in the (econd Ekannplc i But Par^s, multi^
plied by Parts, can ojnly produce Part6. And
the fmaller the Parts are into which the In-
teger is divided, the greater will the number
of the Produd be in (hew, but the le(s in
cffed, as m die following Exatnples.
Example 4. o, 50 Multiplied h}f 0,05.
' 0,50 Log.Q^$Q — OjtfpSpyo
Q>05- Log. 0, 05 >- .i,dp8p70 ;
250 Log. 256 —2,3^7^40
000
000
©,0250
Example 5. .o;o5 MHltiplied by o, 05*
0^05 L<g. 0,05 — i,rfp8ip7o
o>05 -t^^' o>^5 '•■ -'i,tfy8^7Q ^
O0O
0,002 $
' a 8 .. Arithmetical PropyAions^
Prop. 2.
*io divide one Nunibtr by anoiheu
Firft write down the Logarithm of tht
Dividend; Then write down the Log. of the
Divifor under it, and fubtrad it from it, and
the Rcnaainer will (hew the Log. of the faid
Qijptient.
. T^hus if you were i$ divide 5625 fcy 75, you^
mil findtbe ^dtim tobi 75, 4^^ ^bk man--
mr I
the Log. p/ . 5tf 2 5 k 3 ^1 %<S^ 2?.
Tfce hog. ojj'i to befubtraHed if i,875o^r
He^ the Log* of J % ^ ^i,«75c6^
Now though here be a Uoit diiterence
rnore in this laft Log. than in the Log.of 75%
this ftnall difference is not eonfidcrable ; But
i{ you find a greater difference, it (hews there
is a Fradioh, which may be eafily found oul
if you work by Decimal Frad ions.
Ejjatnple. Divide 6^21 by i^^
'the Log. of &^2i ii 3,80078^^
the Log*2^to bt fubtraaed is 1,92427^
Hep Log. ^. — !■- ^ 1.876507.
Now this Log. 1,87^507, is much more
than the Log; of 75, and yet it is muchlefs
. than the Log. of 76 i therefore here muft be
/ a Decimal Fradion found out, according to
^^*^ /he Rules of the Seventh Chapter before.
n . \ ' Turn
Anthmeticdl "PtBfoptnmtw 69
Viirn Ihercfole ©verthe Tabks till -you find
87*507, fiot regai^dfrtg the Characay iftfcki
and you (hall find the Number anfviFitiQg
therennto 157525. Now becaufc the Cha-
raderiflickoi youtLog.^ Is it therefore you
mi^ft take buutbe tf{a .firfl Fibres ;ofcthis
Number for' the Qootient, and the tWo fol-
lowmg^ Figures mak^ k Dedaial -Frtl^lbn)
thxx% ^f(25i*ati^75^ttKkiMpwtftiWhich
isjuftimore* ^^^ ^
> BliPl^e yoa^^idlCike:hted, M^kttfi^
Multiplication, whether Vaur Nui|kb^b^
^hkB ^(£li tlivide be a FM^da dr s^^^fik
thaf ^l> much akcr-^iI^odii<a,\i^d^
-the'L^afikhm be tbcci^th^ -ftnlyiHiftrift^in
the Character iltick. .- »Vi ":. V
fmfiiid Nmkri$$2^ l^lOv^i; - ,un t; .•
<j -tbe^ dtfeQtve Log. ^.,wwwwv.«
7^^ Sum a ,1 .qoi'I 3,87*507
. For J»fl« WMjl coMfxder-^ if this tfmtbe/^
^mi^'dMdiii' -hf^ ^'mimMf.o'^%4X^i
fomvf'ha$ kft than an 'i'MNr' Mi^ Ifi})
30 Jrithmtk(d Prfipopions.^
fi many times U tbs$ FraHim cpntMnid in
, . . ^ ••
Prop, 3.
• Ttf find th S<mare Eett of any Kimher.
"-• .1 .• . ■ ■- .• .■ .-■ ■ '
HaK the Ixigatithtfi of any « Nwnbcf
is th« Lc^titbm, of tfee S^uv* Rg«
< thereof. . • • • , i
,tbe Mtf tbmqf .»'*^-^ '• r^ <i?75«*t'
^bf^i^tbe lttg.qf'i.^> iMebinlni^Mtof *be
fad Numbers ., ■ . ...■
' Here likewife if you cannot find yout
tiogttiifiini- exidiy.ln tht Tables ;- you
roiia niake it^t bij^ * Bcdroa* Fradioi^
, '-as^fedSr* ■^-■/■' '■■••■', - '-
v^ OfllJ* corttraiY, by dooKing Ac Log. «
♦oy-t^tober , y6a tii^t ilie Getiinicttical
.SouatetheifCof." '••■■•--•• *■'"■''"''
\-o^~o,T<^T PlfOp-4:- •:-v..?,s':
/I ^Id^^S4^ Logviiai of the .^jre« tJuoi-
f*r .},c -fe^j^ifo yott fi»^ ha*e the togaiwhjn
up tte p«of!.TfC(jai«Ed» > •„
9 •
ArHhmtticd Profofitions. gi
Example. ls% the, Cnht NmAer given be
Tbelog.0fp26i k — ^-^-"-^ ^9666%%
7'he third J> art iher£of k^ tv .,- i^$zz2jp
ifiphich U the Ldgarhbm ef 2 r , and that if the
Cube Root required*
Likewiie multiply the Logarithm of any
Number by 3, anditproducechthcLogi*p|f
the Cube' thereof. . _
Herelikewife yoiamay makeufe of Deci-
j l^a} jFradlons, whidi in tjhefe Operations are
far ino|ce cafie tfa^n otheri. '
' Prop. 5.
^ Hop to mrk^tbe KhU ofibreet $rthe%uU tf
Frfff^frtion.
The pl^in and common way, i^hich u beft
totruftunto, is after this manner.
As in common Arithtnetick, you multiply
. thefecopdand third Numbers together, ana
divide their Produd by the firfl l^^j^cr : Sp
: heie you mufi add the Logarif^P of thq
fecond and third Numbers together (which
is c^iiivaleiit fo the multiplication of them)
2ind then fubtra^ the Logarithm of the firft
Number from the Produd therepf (w^icbis,
equivalent to DiviGon) fo you have thg Lo-*'
l^arithm of the fourth Number xiequired.
Example,
Ai 6 19 12 I So 2i4t$i^^U
C 5 \' The
-i
§ 7 Arithmefi^4 Prpp^f^t^ff^*
The raaofier tf ihe^ Work ouafi b^4hu«.
\Aj 6 the Log. of 6, which is ^ 0,778 n;;
trt t2*tbB Log. of 12 y rvhich is ^— r'* -PIP » 8 1
So 216 f be Log. of 2 iSi mbieb is ^ 2^3 344.^4
ilo 43 2 Tf-e jfJiw of theft 2 Log. iirg -j 4 13^3 5
' Fr(»m irl^iflfc /«i/. *fcc ftrfil ^ ^ g
• • Log* and tl;zre ftmains^ ^ ^l'^ t '
fri&ici& ftf ii&> Log, of ^^2 J TPbich is the fourth
TermofNttmberdeJ^rcd* *
. Another way to ferform thU.
This work nmay be feme what (horfiied, if
inftead of the Log. of the firft Number you
take the Aritbaieti(;al -CdnDplement thereof,
ists tibdw'ed h^ioit'Chp. 11. and then add
the three fiifl: Logarithms together, and they
produce your defired Logarithm, abating 01
Cancelling the iiift Figure of the Charatte-
riftkk.i .
trample. * » :
Ji SiheAriib. compklog^cf 6isr-9,^2l%^t
3a 1 2 the Logarithm of 1 2 is- — — *i ,07^ 181
So 2 16 ihe Logarithm of 2l6is — 2,334454
To 432 'ih fnm of alttbra^ ^^^^^354^3
whieh^ eancellifig the firfi Figure §f the Cbara*
^erifUc^^ ma}^$ the iMgarithin jufi as hifore*
Prop.tf.
, the Rule of three Keverfe.
Add the Log^khoas of the firft and ft-.
'- A condl
Arithmetical JPropoJitions. 55
cond Numbers together,- and then fubtracii.
,the Logarithm of the third Number out of
them i that which remains will be the Lo^
^arithtn of the Number required^
Example. If 375 Men build a J^attahmt
§ Parl^ in 72 days. In botp t^any days may T3 j
Men maf^ the likgWall ? '1
Ij 3 7S ^en^ Log. -^— — 2,57403 X
JRequin 72 days^Log. 1,8573 32
Sum of tbefe Mb ; 4,43 1 3^3
^^af 133 men ? Log. Jubfr. — ^,12 3852
. 20^ days ^ iKefi Log. a,3Q75ii
y
Prop^j. ,
7^0 find a mean troportional betWHn tiȤ
NMmbiTS.
Add the Logarithms of the two Numbers
jtogetber, and t^ke half the Sum thereof.
E:^flc.
"rbe nHmbeTrgivtn^9 ^/^•—';'^ 5 42 42
^ iio Log* 1,204120
The Sum ^thereo f ■ 1 . 2 , 1 5 83 ^2
^be half thereof ' 1,0751181
which is the Logarithm of iz^ the Mean Ptq^
foriion^ required*
<r^ f fop,
■» , ^
>•
* (
24 Avithmettcal Prapafitumf.
Prop. 8.
Having three Numbers given^ to find a fo^tb
'i ifi dupliaaui trofortion^
Double the DiiFcrence of the Logarithms
M^hich belong to the two Numbers, having
tlhe fame Denominatic^A ; Then if tlie fun
Number' be lefs'tban the fecond, add
that Difference doubled to the Logarithm
of the other Number: fo the Sum thereof
will be the Log* of the fourth Number
r^cquired.
Thm Hhe Superficial ^enfent efi a Circle^
vpheji VUmeier i^ 14 Inches ^ heing 154
fquare ikihesy the CctUent of another Circle
Ufbejfe TAamtter u 2% Inches^ mil he ffund
iobe 6x6.
Diameter 1 4 Inches^ L&g. — i , 1^6 ) 2 8
VianUtetit Inches ^ Log. 1447158
Difference r— — * ,301030
, , ^Difference doubled 3^02 odp
Content giveni^^Log. — ' 2,187^21
Content required 6 16 Log* 2^7 S^ 5 $ t
Cut if the-fiirft Number be greater th^n
the (econd, fubtraift the Diiferencc dou-
bled from theLogaiithm of the otheNiJnd-
ber. /■
Diameter
Arithmetical Prafofitioni. ^ 35
T)iameter 2^ Log—^ 1,4^7158
Viamettr 1 4 Log. -^ 1,14^128
ViffertHce ' '■ ' ,301030
Vifference dmhUd ^602060
CoHHem given 616— ' — i— ^2,78^581
CiHtent required 154 ■■ ■■■* 2,187521
Prop, p.,
Having thru Numbers given^ to find a Jmrth
in a triplicated or Cubical Vroporticni *
Triple <he DifTereiice of the Logarithms
which belong to the two Terms which have
the fame denomination: Then if the firft
Term be lefs than f^efecond, add that Sum
to the Log. of the other Term •, fo you (hall
have fhe Log. of the fourth Term defired.
Example. If s Bullet^ vpbofe Diameter is 4
Inch^es^ ipeigb'ppiunds'y another Bullet i^hje
Viam^ttr is $ Inches vsill weigh 72 founds*
Diameter 4 Jnehtsi Leg* — —0,602 o<Jo
Hametcr 8 Inches* Log* '— — o j^o^ogo
"Difference' , 30 1030
Difference tripled -^90^0^0
Weight given 9 pttnds^ Leg. 0.^54243 ,
Jfeight required 72 pounds^ Log. — 1 5857333
But if the tirttTcrm be greater than the
fecond, fubtraft the Difference tripled from
the Log. of the other Tcifm.
Diameter
\
3 6? Arithmetfcal Bropopttonsi
Diameter 8 I/fcfc/. Ug*^" 0:9030^0
T&anHHr 4 Inchu^ Log. 4* o>oaotfo
'Differmce — ,301030
Vifetiftce Tripled ?pojopo
Weight given j 2 pounds j Lflg«~— ^^,85733}
IFeigbt required, pfoundsy Log. — -0:954245
»
Prop. 10.
il ^fum (/ Af(^;/e)/ fc^wg forhorn for an^ Nam''
btroj learsy to find boxp much it will come
iOy reclaming Intereji upon Iniereji^ according
to any Kate propounded^
Subtrad the Logarithm of ioD from the
Logarithm of 100 and the i«atc added toge-
ther^ then multiply their difference by the
njumber ^f years propounded, and add the
^rodud: thereof to the Logarithm of the prin-
cipal Sum i fo yon (hall have the Logarithm
of the Total Sum which the Principal and
Intereft doth amount to all together*
Example. Wk^ mil too /• being let out
for 31 yean-i increafe to after the rate of
4 per Cent, per An. reclining Intereji upon
Intereft for the fuid time ?
' Firftr' SubtraS 2, oaoooo, the Log* of
190, from 2,025306, the Log. of 106
(vphicb it the Kate propounded) the Remainer
is 0,025306, vifbich being multiplied by ^o
/
Arithntetkal Prpfopicns. 57
y^ars^ producttb ,759180 > vobich added to
the Log. of 100, mak{s 2,75918a, vphich k
the Log. ef 574. ''S 5: So that it comes to
5741-75. . .
Prop. II.
A Sum of Mony being to be fatd hereafter^
to find ppbat it is tportb in ready Mony*
Here tftc Work is the fame with that of
the former Propolition j only inftead of ad-
ding, you muft fubtraA the Prodad out
of the Logarithm of the Principal: Sothe^
Eemainer is the Logarithm of thc^umyou
feck for.
Example. What fe 100 1, to he paid 30
yean hence^ worth in ready hbny^ after the
rsne of 6 1, per Centum ?
Here bimng found the FroduSy as before^
to be 759180, fnbtraS it out of the' Logarithm
of the Princifaly which was 2 000000 i fo
there remains 1,240820) which is the Loga*
rithm of 17(4 11, which (hews the faid 1 00 1.
is worth but ly I* ^ $. 2 d. ^ c^. kvc* « '
Propf
3^ Arithmetical Propoftions.
Prop. 1%.
A ysarly 'Rtnt or Annuity u eoniiuue an^
number of y tars ^ to find u^bat it U wottb
in ready mony^ af any Rate of Jnferefl pra^
founded..
Example* mat U tool, per An. to en^
dure ^o years tfortb in ready fnony at 6 per
' Ccritiim.
Firft, fal^e the Logarithm of too from tbe
Log* of lo^ and the Kate of J^nterdjl added
together^ which is6\»
Secondly, Multiply this Log^fmnd by the
number of years whicb it is to continue y which
are ^o years.
Thirdly, PiWeicol. by tbe "Rate of the
luterejiy which is 5, and it wilt praduce
%6^666^: tdfy the Log. hereof and aeld it to
the former Log. which you foundy and tbe
ProduS thereof will yield the Log. of the
Arrearages , with that faid Sum for that
tithe.
fourthly. Find out tbe true Number of thft
Arrearages^ and out of them fibtraH the PrO'
poriiomlpart vf loo before fmnd^ according to
tbf ftii/r of Intercfi. So you have the bare
Arrearages for that Trofortional fart.
JL^fily, iakl the Log. of tbefe lafi Arrea^
rages.
•
Arithmetical Profojaioffs. 3^
rages j^ and JubtraS fromjhem the Logatithni
found by the Multiplication of years (in the-
fecond Knle) fo jon (hall have the Log. of
the true value of thoje Arrearages in ready
tnony: 'then add to them the Logarithm oftbt
Tthtcipal Sums fi y^ /hall have aLogartthmj^
the tike Number whereof being found $uiy and
reduced into Founds^ ShWings^ and Fence^ if
the tvorth ef the fA^nuiiy defired.
'J^e Logdfithm of 1 06 ■ 2 ,02 53 0^
'the Logarithm of i 00, fubtr. 2,000 000
Re/f/ -, ' 0,02530^
IFhitb multiplied by ^Q 30
TRelds 75PjSq
Add the. L(g. of 1 6, 66* j , i,22ij82p
Soit,mak^s 1,^81005?^
rybfeb U the hog.^ J5572T5 farts.
From trhich fkbtri i6^666'y
Kefls 7P.€)548
1^ Log^ of this Numb. 7^,0548 Ir8p7p2jr
Log. found by muU. of years ^ fubtr. 0,7 59 1 80
., Addihil^og.of ioq\. 2, ©00006
So it makgs '3,138741^
.r^^fichis the Logarithm of i37tfC48> n?l>ich U
\
rtx
46 ArithmBtical Proportions.
In tlicfc.Queftions it will be convenient ta
have a Table to, reduce tbefe Decimal Fra-
ftions into tngHJh Monj^.
t — II >■»■ > I I ■III « ■! I I _ I ■ ' " ■ ■■ ■ II I |l|ll ■! ■ 11^ II.. -
4 fable of Decimal fradum for Englijk
t4ony^ ibe Pound bang dividkd ikio
H P > ^»»»| ! *■
MS
'7,
16
H
12
II
IIO
Vecim. \jh.
*i^
)p5oo
pooo
^QOO
75 ^o
7C0Q'
d50O
6ooo
5500
5 coo
9
8
(5
5
4
3
Vecim.
4500
4000
3500
3000
y/.[ Vecim*
i
2J9C I >?
^000
I poo
9500-
II
IC
9
8
0458
*:
dlVecim^
0417 uL^os^
0375
03 3 i
02^2
02 50'
5J 0298
oi^7
2
'-**-ii-
OO42
Faniings
6^31
COil
ooio
11 ' >ii
V
Or elfeyou may coupt thus, 'The Found. ,
or 20/. being looooparts^ cVciy i5 //being
a tenlh thereof is 1000 patt^,' ahd'everyfbil-•
Ji^g 0500 parts. . *^^*^?\
;. For the J>eitC(s;,:The (hilling beiri^o fpo, tffe
fix pen je is 02 50, which if you -etpJ dflf ffte
rirltand la II Figure 1525 ^ fothc two middle
^gures will be equal to Farthings, only i in
2 5 over. Cemetrical
♦
Geometrical Tropojitions:
Px6p. 13.
ibe Side of a prfeS Cecmetrkal Square hir
ing givcHi to find the Contents
Double the Logarithtfi of the fide given,
fi> you have the Logaiithm of the Contents
required. . ^
So the Stdt of tht.Squfin being 10, tbeLth
gariihm thereof i$ i,oooooo^ which doubled
tnak^s 2^000000, iiohuh is the Log* of 100,
being the Content thereof •
. . Prop. 14. ,
Having the ttpo joyning Siies"^ or Length ana
. Breadth of a Long Sq^arei to find the Conr
tent thereof.
Add the Logarithms of the two Sides to-
gether. , , ^
'ihm one Side being^ 20^25 or a quarter^ and
the other 3 0C7 5 partSi or three qnarursy
' T'be Log. of 20(2 'i it i53<^^42 5-
7'be Log. of 3 0C7 5 is 14 87 84 5^ ^
T'beSum v 2.7P4270.
- is tbeLog.4f4i22^4p parts (trc^ which if tbif
' CQntent.
^ - Prop#
4^ GedmtHcal Propopions. i
Prop. .j.
Tthi Side of a Geometrical SqHotebeiHggiviiiy to
makf another Square which fiall contain it
2, 3, 4) 9f any Ntimber of times as r^uch more^
ior lefsi or according to any other troportion^
Firft double the Log. of the given Side, Co
yo* have the Content of the Square. Then
increafe or diminKh tho Contents by the Pio-
portion deiired. Then find out the Log. of
the Contents fo indreafed 6r diitii^tflicd) and
the half thereof will be the Square Root;
n^hich IS the Length of the Side deiirt d.
Example. Let the Side ^iven be io, thk
Content thet^eof by Prop. 13. is 100. Let il be
rehired to ma\e a Square 3 times greater^ then it
mufl contain 300. Nqw the Logarithm of 300
U 2347714I, the half vpbereof U i5238570>
ii>hkb is the Log. of 1 7,3 2 parts very near.
(
Prop. 16.
* • « . ' . •
In a BSght^angled 'triangle ^ having the ttpi
Sides mal^ng the Kighi Angle^ to find th^
Jloafing Side.
. Firft, do^iblethe Logarithms of thecw6
Sdes, fo you have the Log* of their Square
fcycialiy
Geometrical Prb^dphns. 43i
fcverally \ ivhich Numbers being foundf c»uc>
tnaft be added togethei: bv^Comanion Arith*
tnetick, and thefa find the Log. of their Sum,
the half ivhcreof is the Lbgarithnn of the
SidcdeGred.
Exartiple. tit the ti^ Sides given he 30, ^
' and 40. . '.
Log. of 30,i,4y7i2 1 Log. of ^%^i^66io60
doubled am. 9 '^4^2 ^2 and 3,204126
Jfbieb dre Log.of f 00 and lio»
fThkb added togetBer ma^e -a 500
^hehjjtpbereof being i,<5jj^^70
k the Log. of 50, which is the Rooty or Sidetf
the Sptare required.
In like manner you may find the Diagoiml
'dr Ciofs-line, teaching from Corner ccCor-
ner of any true Square.
Prop. 17.
in a tLebangular 'trisngUy. himng iht j^ft
Line^ and one of the , ftrdgh Sidis^ to find-
m the others
* I * .
Square, the Sides, arfd tubtraa the leffet
Square from the greater Squard, and the Re«
hiainer is the Square oii\it remaining Side.
Exawnple. Lit the flofe Hide he jp, fnd one
if fbefirai^t Sides /^Oyto fitid the otber Side.
D The
^be Sxjuare kifii.ii , . i6qq
tfincbJiAtraBfd^tbeter^s ' f^o
VlffUg. of poo is. 2,9 S4H^
^be palf n>hereof is ' , fiP77lil
pjncb is tb^ h»^*o( 30^ md.ib^tis thi timn
S^de required* i
^ , The like will be perCbiiDed by the other
' 'side.'' [■' ^ : " ^ ^ ;,^. :
Prop, ^8»
Having the' ttv$ Jfraiibt Sides of a. %fQ4Hgti*
larTriangte^ io^ find tbe Conttnt theretf.
"*'\ " .» *f • • "i ' c • ' <
1^. ... I ■ • ' . ' .
Add the Logarithms of the two SiScs to-
gd A^r, fo you have thie Log. of the Cpntciit of
-the \v66le Squares then take half that Con-
tent, and it is the Content of the Triangle.
Ttbus tbc Sides of the 'triangle being 30
IheLfi^ofiois \ , ^ 1477121
^heLoff^^ Lois'" i.6oiodo
-1th Sum is ; 3,i07i?l8i
»wc£> is tbe Log. of 1200, ffetf balf wbert-
^ V Ao^^xehich is tbe Content of the 2>i-
'Or elfc ytbu may npultipl^ ope Side by t|»c
« , W'of the ot^ici;: ^s!f^ 30 nmhttily^d by ao
\yufdf,6oo'^ <4f ^>/are, And this is % ic^t^
df ihe DMafuriog c^ all. Triangles affet this
masDier, by half of oqe of, the §id<is, by the
othct*
Ttmeafnrt the Content -cf guy flah friangte^
T^e common acd beft way is to let fall ^
t'erpeBdicular upon the lot)|cli Sidc^. and fo
oniltiply that Sid^ and the. PerpendicMiar
to^ber^ theonebjfchehaif of the other*
jLei the longefi^ Sidei of a Triangle, bt 2^5^
and, the pi^rpendicular (from the ^Hgfe opfo-
fed thertiinuj be 12. NfyJii^y 2 J by 6^ ei-
ther in Simple tiumhtrs or Logarithmic fi
yoH have the Content of the irian^le* *
Multiply 2^ Logi h3979^^
by 6 Lag. 9.77815*
Content i 50 Leg. ^ 2,1 7609 1
Prop. 20.
'J^th thee Sides ef trianile ta find tbi
'- » ' .
This \b anwher ^ay/ though not to ufe-
ful as the fotnay Aj^^ the three Sidles toge-
ther, then fromth^um thereof fubtrajSt eath
Side feverally, and note the Differepces ftooi
the faid half Sutn of the Sides. Then ^rite
p a doifTtf
A.
46 Geometrical Propofiticns.
down the Lc^at ithms of theft four Nombers,
and add fhena all together. Laft of all rake
half of this Sum, and it is the Logaiithm of
the Content defired.
Exannple* Lt% the thru Sties of the Tri-
anglehe 15, 20,2$ 9 ibiir wlfoU Sum is ^o>
the half Sum ^o.
Tfee half jSnm 3 o Log. tj^JJ i a i
Ttbeone Side j^7t^ C15 i^iyto^i
7 be other , 20>ll^.<io i,cooooo
7h third 2$Sp^^C 5' o6p^yo
• The Sum of aU four 4^352182
i%ebalf Sumis 2>?7tfo^i
tipblcb is the Logarithm of 1 50, being the Coh*
tent of the [aid triangle*
'^ t —
Prop. 21.
'to find the Connnt of s Circle the cMh-
: I moH way*
Multiply half the Circumference by half
the Diameter.
' Exatpple. "The Circtmference being 44, and
the Diameter 14, mlUdfly 22 by y^ the Con*
tmt mV be found 1 54-
• This way is n;ioft exadj and ready, provi«
ded the Diameter and €«SbuiDfereDce be tru*
ly known, for which confult the following
Piopofitions.
Prop.
Qeoptefrical Propophnji. 47
Prop. 22.
T3)€ JHsmetif tf a Cmtt h^$ig ghm to find '
the Circumfewiei*
Example. Jii^^o/e tbt Viamftfr pven to-
he 1^.
Sojke Diameter I j^. to. tbiCkcHmftrenet 44*
T'c 3 . 1 4 1 ^, v^bofe Lojif a o,4j^ /i^i
Sotbe Diameter i4^JLeg. 1,14^128
. Jq the Circumference i^ji^jtjf
which U the Log* of J^^^t'^i vAich is alm^
44, as the common TPMy. ^ '• ;
. The moft exa^ Proportion of the Circum-
fcr/:nce to the Diatneter is that ofFsn CetilcHj
who makes it as I to 3, i4i59)2^535>S^7^3^
2314^^ 3^433 > *327P, 5^*8' » but th^ for-
fner Rules will lei vein oioft Operations/ \
'- '■ "■- ' ' ' ■ V • ;• • • ' ^
Prop. :?3. . .;: ;
jKiw«g 1^ Diameter of a Circle^ U find the
Stsperficial Content*
Asi^toti^
SoSquateof Senadiametety to the Omtentf
So Jft the Semisliatneter he 7, the S^tare
^hereof is 4f ^ aid theContent i S4*
D 3 Ot
4B <jedk0etticdf Prif0ftimA
Or elfe focnewhat move Artificially and
Exaftly, ':^'
Ai, U tit l^ I /iti(yS»hf^ tag, i$ p9497t5l
So Sqn. 4 Stnndk J.\ Sif.i9) Lfig. I ^690 196
. ^0 sbe-Logf if fki Conttnt. , • 2 > 1 873 ^7
which U the Log^.af i$39i pdttt^ which is
fimewbainmeexaS^aniheefheu
Xh.Qvciinferenc^\f a Crrch giviHi ta find
. , the IHimettf. ' ^ v
rAs2^p'j': SotheCircun^^tQtbeTHamfter. .
Oii Asa 40 xDjj i ^| r^wM* JL^g. is ^ p^5 02S37
JC^ thtCircumferencc U m Vi^niiUr. * '
• . ^f^^^f Ci^uti^fup^e to pni m Conifnt.
Ji'4 times 2iym ? i ' '-■ *\-
% So thi Square of the Cirtumf. f» tbt ConHHt*
pr, As 1 40 O5O7P 6^ whoft Log. ii — i ,9009 1 3j
So^ thf S^repf th^&mnfr*:to the Content.
'• ^ ' '• vtop.:k6. '''" '' ■ ' ^ •
By tbeCoHtCHi of a Circle to fini thpTAan^n^i.
As 22, io/L ti^s 7, wbick is 28 \ -
So tii d^f^mt^ ^^ ^ Sifsatt dftbeJH^meter^
" * ProR
Giometrical Profhpions. ^
Prop. 27.
By tlje .Cof^eiit to fihdihe CireHmfmnei. '
Soihidomntp tht S(j[uattof tht Cin^^nfif^^ . -5
Cfr, jis i,*o \iy^66^^whoftLogAs 1,0^8213
5^ the Content to the Squ^revf Sh Circumf
» T
V I
Ky, «fe Cmtmtf f Circle, jTa )&irf. tie S¥e^
, dS^Mre fqualio ju .\.
Extra A the Square Jlpot of the Content,
by taking half ri&T Log^thm of the Con*
^M»
Jijf the THameter of a Circle^ to find tbt Side
' cf the Sqiidh^tqual to the Circle.
^s i^ o>ftg^(i27^ iif&4!^ tig**/ '-o.^:^$4'$
SotbeViamettfUtbe'^''' - - -
Prop. 30; '
^j the ViameHr if aCwctt, tQftnd.Afe iHeef
ibeikftriked Sqm)e^\
At lyto 0^707 i'C7, irfo/e t«girr— o,S4p485
5^ ii f ^e Viamtter $0 the infcribed Square*
D 4 Prbp.
50 Geometric Propoftiw^i
Prop. 31,
By ifee Cireumfitfenie of a Cifc/49 1^ jEita tpe
Side of a Square equal to the Circle.
<g(> «i5fi? CircmKferenceU the Side of the SqiMru
v.*
' Prop. 32.
fbtmg the Circunrftrence tfa CircU'i to find
the Side of the Infcrihed Sqitare*
Ms \io W 22 <c7p, whofe Log. f/— 0,352334
So the Circm^mHce to the Sidey &c^
I "
Pfop. 33. i, •
As I ^^017853^8, tipbofe Log.is — 6,pS J0%j
80 the Proportion of the Septate dtatm aboau the
Circle^ to the Cirele iHclntied thtreitt.
'"' ^* ^ ■ . ?^PP- ?*• •' ■. ••' . '
As 1^10 1)273240, whofeLog. is 0,104910
So^keErofortionoftbe Citcle dravm 4hdui tbe
' , Storey p tbtincluded S^re*
. v\ ; .'
Prop. 35.
Having the Axis or Diameter of a Globe^ to
' find the , Snferficial Content. ?
. ^Multiply the Piipjctcr by; ^ Cirfufnfe*
\ I
Geomtricd Pri^c^H^ns. $i
Orclfe, jifj to 22^
So the Sguare of the Apify ft) the Snferficial
Content. ' ^ .-,
- T-y 22: 1 Sq* Axis 1/^(1^6)61 1^
Orclfe,
Asuto 5 , 14 1 tf , nfbofe tog. is o, 4^7 15 1
Sb tf?e Square if the Apds^ tQ the Stfffrficial
Content* \
Prop. 35.
Fy *i^e Circtmftrence of a Chbe^ to find tie
Sstptrficisl Content tbereofi
jIs :j2, #a 7 ' ^ ;
So the Square ef tbt Circumference to. theSu^
ferficht Content.
Ot^As i^to 0,3 183, R'feo/J tog* i/— 0,502837
So the Square of the Ciratmf. to the Content f
Prop. 37..
Bf'th^ A^s or Diameter of a Glote^ to pn4
the Solid Content therof.
/■
As 4 times 7 i ifpbicbmal^s^2^to2t
^0 the Ctfhe of the Diameter to the Solid CoH^
tent (f the Globe.
Ct^As 1 to Oy'^2 ^6y»bofe Log.is—o^jitpff
$^»tbi Cube Diameter^ u the Solidity.
Prop<
59 Qeifnetrfcal Pr$fajitians.
$
'/ . * . Prop.'jS.
By tbi Circunftrenct, 0f a GUhe^ to find the
Solid Contenu
As \iioi>p\6%%T^ »h^e Lofr. if -- 1^21 J ^f^2
S^^hMM^of'ibtCifcwttf. to m Solid Content.
:* ^ Prop. 5p.
Knmrittg the Solid Ciontent of a Globe^ to maj^
a Cube enseal to the Globe. . ..
£ktia A the Cube Root of the Solid Con-
tent of the Globe, which is dbne by taking
.a third part of the Logarithm of the ^Hd
O^icatv^f the GkAe. '
-~ ~ -i '
Ptop 40^ ^
1^ the Aoth tf a Ghbe^ to mal^ a Cult tqnal
to tbo Solid Content thereof.
Aa Xy to o>8g<04,- phofi Log* it —0^0*^57
SotbeAxh^ totbcCube Koot* *
Prop; ^.T. ''
ty^ the Ctrtfmference of a Globe^ to maf^ d
Cube c^ual to the . Solid Content thereof.
As I , to^ 0^2 $6 5 5^ i wJoqfi. JLog. is ^ o^^\ 80
So the Circumference^ totheCubefioot^
Prop.
V
Prop. 42# •
iBy the jfxif (f a GU>be^ to mahf a Squart
equal to ibe Superficial CBntent tf the Gloik*
ft
As i,*iM,772454,»^i&#/eL<ig.i/— 0,248573
Sa the Axiu to the Square Root.
»
♦ Prop, 43.
^j Ai Ckrtiun^etenee of a GliAe-t I0 nkalks ^
Square equal to the Stiperficial Content of
the'&ohe.
•jv. -
Ai i^uOj^4^i%9,»hofetog*is^O^'J^^2^
So the Ay^^ to the Square Km*
• *Piop» 44. ;
2i fueajitre the Supet^tiaP Content of tht hiaif
of a Cifchy ot of any SeBkn rf a Cirek
more or lefs than the half*
MaMpli^half of tbci Compels thcfCDf i>y
the Scmidiatnectr of the Circle.
Example. Supfefe a Circle^ the Diameter
thereof being J ^ \ jp tht Semidiameter u y\ and
the Compafs of the half Circle wiB he22\ and
the Content of the faid half Circle is required*
Muit^ly half the C^afs giveUj mbich is
II, by the Semidiameter 7^ jithtGentem u
found Mi^ 77^ ,; - ^
' The
'54 Qtometrical Propopum.
The like Rule holdi for any part •f the
Cirde, more or Jcf$ than the half, where the
5ei?jidumetcr is given : But «thcr Sedions of
Circles cannot well b^ fouqd, without the
Diameter be firft found*
Erop. 4$.
io find the whole Vianuttr ff a Cirtle^ by
kgiomng a parfAereof^ and the length of the
^ 'Cb$rdcr0fitig the Viamner in that fan.
Let a fmaU pari of the Viamefer be 4,
, and let the Chord interfiltiftg it ie i a f .
* S^iire one hal£ of the Chord;»wfaich is 6^y
that is, multiply- it by it fclf, ordoQble the
Logarithm thereof, and it produceth 40 »*
which divide by 4 the part of the Diameter
-^ireoi and there . rcfts 10 » which added to
the faid part> (hews the whole Dianf\eter to
be 14.
This Rule holds cither for the SeAion of
Ike Circle, or for the Sedion of a Glebe.
Prop. 4^.
Tto find the Superficial Content of the Segment
of a Globe*
Find the Diarrieter* as in the lafi Prd>lem »
fhen find the Content of the whole Globe
thejTcby , as in trop. 3 }. and theo fay. -
, Gtpmetrical Prapepionx, 5J
At the H>boleT)iam. 14, to the Superf.Cotit. ii6
So part <5f the T>i»m».j^to Contm thtreof ijf.
Prop. 47. ,
tomeafun the Cmm rf tbt Stgmttt of ».
Circle,
Mcafiute the Chord A B 1 2 f , and the Per-
pcndieulatpC4, *.d multiply the whole
oi the one by two thirds of the other. This
will come very near, as you may fee in mv
Pm-ebafers Patten*
Prop, 4$.
7o meafitre aa Oval Superficies.
^ Multiply the Length of tht Oval By the
Breadth, and divide the Produ^ by i.ayij 4.
whofc Lqg.iso,io4pio, and the Arithme-
tical Complement thereof p,8p 5000.
Or by way of Preiportion,
•f' 1,37324, ro lie l«»g,i..
^<'*»t Breadth, to the Cment.
;« J rt* ^/.'^' Ifgthcfihe Oval be
iO^Hdtbt Breadth 3 o, mat it the Content ?
Sjtbe Breadth 30 Log, 1,477"*
"rotbe Superficial Content ^2,074,7*
«*«efr, cancelling the Radim, it the Ug/^
9\*A^ partt, p,op^
Ho meajkri a fglyfou^ or a Kegulat Suptrficiei
that bath many equal Sidtu
Multiply half thyCoippals by the Length
of the Line difawn from the Center fquicc-
wife, to the miM •f any of the Sides.
Examplei Ln^tke Myg^n h^yt Jbe eqifd
Sides J ioeb 24 hfigs the JLim^ dratm fr^m ttk
(enter to <ihy ef, the Sides fimreii^ifi^ mU ht
2 1 fere : So half the Cempsfs mA be | titms
a4> vpbicb is r/i > tbis multiplied by 2 1^ mak^s
1 5 1 2 for tbe Contents
Prop. 50* " , >
Tto futd the Sttperfieial Cqn^^nt ef a Cyliadir
by the Diaimter^
Js *j t$ 22i otjAs^i to ^ii^iS:
So tbe Viamtter and Length of tbe Side mnltU
plied together, tinhe SttferftciaJ Content a/the
em- fide of the Cytinder.'befides the ttpo Bafes^
j£ sample. Let theCiameter be 7, the Side
Of Length 12, which muhiplied ma)^ 84 '
Asi^H 3, 1411^:; So%^to26'^y%f^.
Or clfe you may work k fcDmewhat cnojre
ircadiiy by Inftruments.
As Q>3 1 8308, to the T^amet^ 7^
Sothe Length 1 2 ^ to the Contem 2 4^4 fere^
And by the Tables,
As 0,3 1*308 Ariih^ ComfU Log. 9.497 f 55
tif itffi Diameter J ^ Logy 0,845098
Sa^ the Length 1 2 , Log. i,Q79l8i
*taibeCoHteHt26^,%p. -^^4^14^ 3.
fr(miPbkb the Kadiks beittg fuhtraSei^ ther^
rematHs the Log* rf 26^, %p parts, a§ before\
for the Conieht of the round out-fidej not rei}^^
niftg the Mo endsy %»bicb you may find by ^
fropotim of the Diameter to the Circle*
But the bed and plained way is by the
Circumfefence, which being multiplied by
the Length, gives the Superficial Content, '
adding the two ends thereunto. ' ^
So the Compafs being %2y rrndtiflied by\it.
malfis 26^, mthoat farther trouble^ bejide tbf
ends* ^
#
Prop. 51.
tafietd the Solid Cont£Ht of a^^Cylmder^
Fhfi; iind the Content of the Bafe, by the
Rale 0£ttie Circle, or Diameter^or bdth i then
ipttliil^y the Contciitthereof by the Length.
EiOjfnpk. Xet the Cylinders Vhmeier bej^
andibe Lnt^ 12 » ihe. Content cf tbe fi^e m^
be 38i tete, viz. ^i^^^^'y^iMcbtpnh^lkdfy
M^nuiiis the Solid Qfutem J^6iy%i^ parth *
- Prop*
58 GtQMStrkal Propofitionsm
Prop. 52.
iV fiudtbe Super fiwl QmHHt ^a C<M.
Multiply tl;ie whole Sidd by half the Com-
^^{% of the Bafe/ adding the Plane of the
iafe thereunto.
Example, ibe Compafj bang 22 ^ th Side
12 *> 12 multiplied by 11, n^hkb is half the
Comfafsy yields 132 for tbe Superficial Con^
tent of tb^ outfidey mtbout the Bafi*
Tto find tbe Solid Content of a Conei
^ Firft, bjr the Compafs find the Plane of
tht^ Bsife ) then mulciply it by a third part
of the Height of ihe-Cohc.
Example, th/ Compafs being 22 ^ and tbe
height 12, /ir theConieHt.-
- Firft, for the Content of the Bafe,
As\l2^^66i7,Log*CmfUAriih. i,poojpo
Xo the Circumference 22 Log* 1)34^ 422
So the Circumference 22 Log. .^^34^2?
to tbe Content of tbe Rafe '^^'5^5^14
tifbicb eanceUng tbe Radius^ h is tb$ L0g. ef
3^)$' 53 > ^r^hicb kmg multiplied by a tl^hrd
part of the Hxight^fpbicb is 4) makfs 1 54,0^1 2
parts*
. Hf re you cnuft obferve, That the iJeight
of
Geoxtetirical Pirapopicns. 50
of the Cone is not the length of the fidelinii
t^k^ on the out^fide, from the Eafe tb the
ibaip Point thereof) but the Line that falU '
perpendicularly, fron^ the flbarp Point, to th^
^Center of the B^fe, all along thtough the
middle of the Cone, which cannot well b^
mcafured, but may be found out by the Se-
midiameter of the Bafe^ and the iide ot
flope-line on the oit-fide, by the Rule of the
Square, ai^in trof. r^. . •
"Prop. 54.
> ■» ' ^^
Td tneajure h Vyramiie*
You qfiay bbfe/vc hete^ f hat a Pyrami^c
differs firorh a Cone in' this rcfjped. That a
Cone hath always a round Bale and Super^*
Cits; like a Sugar loaf i but a Pyraniide hath
an Angular Bfafe Ind Su|)erHci^s, 0(4, 6y 8,
Or any dumber of Sidesf* ' T6 tneaturc this
cberdbre, you muft fir ft find the S'uperfiicial
Content of the Polygon at the Bafe, as m
Tr0p. 47. then tnaltipl^ that by a fh&d p^t
of the Height.
Andrhtre alfb the Line of the Height can-
Aoc be theafufed on thd ou(-fidei but muft
be found but by the Line drawn froa| the
Center of the Safe fquirewite, upon the
tniddle of one of the Sides of the Polygon,
wd then f roft) thetkce uii^ f be toiddle of one
E rf
6p UJ Tngfrnommy.
o£ the Sides, to th&C«ify ot Point at the top
By thefe two Lines you may by the|^Qle of
theSqaacc, Pr$p. i6. find the infideLiae of
the Height, and fo find oat thc< Solid Con-^
tent theieof*
THE
1 •
life of Logarithms
IN
'TRIGONOMETRY.
» . • . * •- '
HErcin indeed conGft.« |thcir mpftfiequent
and moft excellent Ufe : Fox as Trigo*
' hothetry is neceflary in moft patts qf the Ma-
thiematicks, fo it is fomwhat difficult smd
' tedious to be performed by Naiutal Nuin*
]1)crs and Arithmetick*. And thpygh many
Mathematicians have found put fptn^ helps
the];cin, by avoiding Divinpn id cifiis^y Ope-
rations v yet none comparable |achi$ of the
, Loprichnis« For> firft, thefe ArtiiMal Sinc»
' dnd Tangents are found as. readily as the Na-
'tiiral Sines and Tangents, which muft fcc
* foflfidout by Tabl9s, it being injpoffible fei
^
Of Plain TrtMfigUs. fSt
ny toteep thetn in rneroory : Ami then being
X ' ound out, they are aseatily tranferibed. And
laAly^ the Operation is abundantly more {|>ee*-
dily and ceiftaii^Iy perfermed by them^becaufe
here is only need mofi times of the Additioa
of the two found Numbers togetherf or ac
moA but a Subtra6tion of a third Nfumbet
. from their Produd, or inftcad thereof, ail
Addition of three Numbers ti^thet.
Tf iangle^ are either Plain or Spherical.
t Of fiainor Tiithf- lined tnakgfu.
HEre, firft, take a^ iivn general - Rules ah
bout them.
f • A Plain or Right4ined Triangle is ' 4
Plain or Superficies contained or compre<^
headed within three Right ot fltat^ht Linesj
loyoed fdgether with three Angks or Cor*
nera,
2. Thefe Plain Triangles at<! either Ri^t^^
ai^gled, that is, havii:^ 6ne Right Ai^gl^ as
Wig. t. ABC, oreKeOblique-Angled^'tfaot
i$y Without a Right Angle, as Fig* ); ABC
lisving all the three Angles eithet Aeutie,
Chatis^ te& than y o i/^f . or dfeone ofti)enii
Obtufi^ 'that is, mdre than f o i4g;. ^
0. In either fortef ibefe Triangles the I
Angles are always e^ua) to two Right Aii^esi
rintiS) t%i»iig%
69 Of Plain TrungUs.
4* In a Right -angled Triangle^- ck< Rtglpi:
Angle being always §o deg. the other two
Angles fnake*alfo jaftpo^kg. in fuchnban-^
:ner that one is the Pomplemeni ot Confine of
the other > fothacan^of them being kaowo,
the othei h alfo kn^wn*
5« The LiQes aboatthe Triangle, (bme
call them Sides, fom^ Legs: But in Right*
lined Triteglts, for better djftindion, it
^ill >e beft to call BA, the bottom-line,
the Bale > CA, the upright^ line, the Catbi-
tus fit Perpendicular ^ and BC> the fiQp^
line, the Hypotenufe.
^- ^/ EVety Triangle hath (kc parts 9 4hat is,
three Sides )and three Angles \ and thefe are
aUproporddnal one toanothet: fotbatjany
-dnxe of them being knom^n, tb^ otber thi ec
^ay be fbiind puty unlefs it be the three
-4«glcs«f a Plain/Tri^ngte, which oaly (fa^ws
the Proportion, but you may make the Mnc$
^hatfetgth yottwillf
: psJ TheSinei of the Apgl^sare prO|?c>rti-
xaiarto their oppotiie Sid^sv and th? Si^es
^efpitportionaj to the Sifies pf ib^ir 0ppofiu
^t^tes.. . ;,
U $f p*wtM^i as y0H p$fll ftfi iy tb^
t^H^fa^y Angiee4:<^6d^oir£.£2^
out of 186 ^^ and work by th^ Stpc t^^eiec^.
:il ,^ " i' ^ Proj
»> <
t-
■ c
%
IjctnfetnAj^Cf^R. ^ ;^
Of Plain Triangles, . 63
« •
Prop. 55.
^m Anj^Ui and mt Side of a Kight-Mgh^
Ttriangti being giviHi i9 find the otbtr
Sidei and Aifgle.
f^ Examfk. In the firft f igutc, in the Right-
^iingled Triangle BAG, the Angle at Abe*
ng known to be a Right Angle, or 90 deg»
and the Angle at B beii^ known to be 36 2.
52.ifiiff. 12 fee. and the Side B C being
known to be 3 50 Inches, Feet, Yards, Poles,
Miles, Leagues, or any other kind of Mea-
sure 'f Hew may 1 6nd hereby the other two
Sides, and the ether Angle ?
Firff, to lind the Angle unkown, which
is the Angle at C, you vrnxA remember the
fourth Rule before-going v And fo this be*
ing a Right-angled Triangle, the Angle at Q
is the Conaplement or Co- fine of the Angle
at B. Take therefore the Angle B 3^ ^. 52 m.
12 /fc.outof $^odcg. and there reiis for the
Angle at C %^d. ym. j^%fic. which is the
Co. fine of the either Angle.
Secondly, to find the Side C A, your bed
way is to work by its Proportion to the Angle .
oppofed thereunto at 6, according to the Te-
venthRuIe 9 for this \$ a general Rule in all
^lain Triangles*
E 3 ^#
$4 Of Plain TrtMgUs.
, As the Sim of any Angle^
to ibe Parts §f the Side eppofed 'tbereniM ;
So k the Shte of any other Anglty .
# "totbt tarts of tbtSidi^pp^tdAmmto^
And fo on the conti^iy.
As the Parts of any SUe^ &e.
So that in this Triangle BAG, having the
Side B C 3 $d, oppofed to the Angle at A
fodtg. you may theicby find the Side AC,
/Which is oppofed to the An^e at B^ that
An^le beii^^knowB to be ^iidfgf $x nm
1 2 Tic For,
As the Radius or Sine nf the An^l , ' ^^^^^
ghat Afoi. 3 ^
1^0 the oppofise Side B C 3 $o 2, 5440^8
So is the Shit of the Angle ^ B? ^^j. -j
^td. 5a i». «2 fa, 5
^0 tbe^ oppefite $ide A C 2 lO ;r2,3 222 1 j
Add the fecond and third Numberis toge-
ther, and from tbeit Sum fubtraft the firfi i
ivhich becaufe it is the Radius, it is done b;
cancelling the firft Figure ^ 9 fo the Recnainei
IS 2,3222 ip, which is the IfOg^of 210 fox
fheSldedcfired.
Thirdly, By the fame Rule you nnay fmi
the remaining Side B A, which is yet un-
known, by its Proportion to the oppofite
Angle at C, which was found to be 5 jt dig
f tnin* 48 fee. .
Of Plain TrioHgks. 6^
Ai tbt Kadius or Sine of 90 d. 19,000000
2« the Suit ofpofed B C 3 50 2 , 544068
30 the Side B A 280 '^3)447 1 s9
^kb caKeelUng tjk Kadiwy the JiemaiMer is
^e L(^. of 2$o, for the . Side 6 A. And
thus you have found all the fix parts ofthie
Ttianglc.
< « *
/ Prop* 5^. .
Tp^o Sides and one Angle ef a Rigbi^mgkd
Triangle being given ^ to. find the reftof ibe
TarUefibefaid Irian gle»
m «
If the Angle given be oppofed unto either
pf the given- Sides, you may work by the
Proportion of the oppoGtp Sides and Angles.
For,
As the Farts of any ipomn Side^ ,
- 30 tie Sine of the Angle oppofed tberettnt^ ;
So the ¥atts of any other Side^
to tbt Sine of the Angle oppefed thereunto . .
. 'Example. In the Triangle ABC, tig. r«
Let the two given Sides be AB280, and B
C 3 50, which Side B C is oppofed to the
Angle A, bdngknowntobepo^f^;
Firfi, To iind the Angle at C oppofed to
^hcSidcAft.
E 4 -^f
66 Of Plain Tr'uutgles,
^ the Side hCi 50 Log. *»5440i?!
70 tktfippofite AjtgU A 90 d» io,ooooo(
So the Side kZ 2%o - '2,44715:
iJuwi 1244715 1
4o ife^ Si«c 0/ f^e Angle C 53 ^. ? ^^
' 7«i«.48rcc. ^ ' ^9^030:
Add th'e itcond and third NumberSs ant
from the Sum thereof fubtrad the firft, th(
Remainer is the Sine of the Angle deGredJ!
wh»ch is 53 deg. 7. mttu 48 fte.
Secondly, Now this Angle beiag known^
|be Angle at B is the Contiplement thereof,
«hii:h is ^ddeg. 52 min^ la fee.
Thirdly, For the Side C A, having found
the oppofitt Angle at B to be 3,6 deg- 52 min.
.12 fec^ 'you may beft find lt> as before, in t^c
hft Prof>ofition.
J J the R'mdm ur Sine of the An- 7 ,^ ^^^^
I. . A ^ J > 10,000000
gk at Pi 90 a. 5 '
^0 the off tfite Side ^C 3^0 - 3,54406$
JS0U the Sine of the Angle athl 773 mrj
^6deg. 52 /m»« 12 /?c. y ^^^^ ^
lotheSide AC aio ^2,322119
:. Ypu might have found it atCo by the
$ide AB, and the Angles B and Cv but
to work by the Radius is fomewhat the
|fcadicf way. '
Prop
./
Of Plain Triahglet, 67
Prop. 57.: \
/»* J^h'^gUd T^riaftgky the ftPo Sides in-^
• fludtng the Righ'j4ffgle being given y to fn4^
ibt reft (^ the farts (f the T^riangU.
Examph ^" ^^^ Triangle B A Q Fig' 2*
Suppole the Side B A to be 2S0, and the
Side AC to be 210, and the Angle A be-<
tween them to be a Right Aingk fio deg* to
find the other parts of this Triangle.
You tnay ipake either Side the Radius :
But w$i wilLfuppofe xhe Side 6 A to be the
Radius i fo the Side A C is^he Tangent of
the Angle at B i the Angle at C is the Com-
plement of the Angle at Bv and the Side
B C is the Secant of the Angle B, or elfe
inay be found by the Rule of Oppofition.
' Firft to iind the Angle B,
jiythe one Side B A 2 80 Log. a ,447 158
T'o the 0tber Side AC 210 3,3 2 22 if
S^ is tbi^adm fO deg. ^ ip,oooooo
Sum 12^2221^
^o the iang* of^ d. 52 i«. 12 fec^ ^,87 506 r
fvhich is the Angle at By^ the Complement;
whereof being ^^deg*. jmin* ififec* is the
Angle at C .
- - : ' Then
$8 Of PUi» Triaigles,
Then for the Side B C,
'At the Sine if the Angk B 31^ i. > __• -
Kt milt, 12 fee. 5 y'^y**^*
To its ffppofite Side A C 210 2,32221^
So the Kadius^ or 90 deg. io»oooooo
Sum 12,322219
%Ui ffffpiftte 5i^B C 350 2,544058
Or you may tind chef Side B C, as it is the
Secant to the Angle B.
Ar the Radimy or 90 deg. ' o,6ot)ooo
T'ii the Side B A 280 2^447 1 %%
So the Secant of the Angle Bjtf ? ,o,OQ<Joit)
; d.'^2nu 12 feo. J ^ ^
Ho the Side B C 3 50 , ^2,5440^8
^ If you want the Secant^ you may find i%
by the Arithmetical Complement of the Co*
fine^ Z% Chapter i|.
Or elfe you may fquare the twro Sides, and
then add them together, and the dquai^e Root
of the Produft will be the floping Side B C,
Ibe Square ef z^ois, 7 *40®
Jhe Square ofzioU^ 44100
V^bicb added together makf i a 2 500
T^e Logarithm whereof is 5)088 13 tf
TPh half whereof is 2,544,058
wkieh U the Ij>p ^350, the length of the
iffird Side BC. And thus you bare all the
Parts of this Triangler . ,
Pxop.
Of Plaift Trianglps, 6^
V
Jh aBigbt^OHgled Triangle^ two Sides hang
given^ including one of the Acute Anglesy
to find the other Parts rf the triangle^
^amfle. In the Tr jangle A B C, Fig. i.
Let nhe Side A B be 2 So, and the Sick B
C359^ and the Angle included between
them ^6 deg. 52 miu. 12 fee. to find the
other Parts.
Fir ft, the An^e at A is 4 Right Angle,
or 90 deg*
Secondly, The Angle at C is the Com«
plemcat of the Angle .at B *> therefore it is
55 d. 7 m. 48 fee ^
Thirdly, Thefe being known, the Side B
C roay be found by the Angle B oppofed
thereunto, as before.
jls the Jisdius $0 deg. 1 0,000000
^0 the Side oppofed 60350 3 , 544068
So the Sine of the Angle B 36? 778i<t
• ■ ■
j-Q the Side PlC 210 ^2,3222 ip
Thefe are fnoft of the Cafes of Right-
angled Triangles 9 or to thefe Rules
fbey nnay be all reduced. ,
Of
70
Of Ohtt^ Tritm^lei
Prop- <p.
'tm Angles ef anQbli^ InoMgk bdnggt-T
vMy and a Side nfpafed to either ef tketHy
to find the riji of the Tarts thereof.
l^xample. lo the Triangle ABC, Fig. 3.
the AngU at A'S30. the Angle^atBiUSj
ana the Siie BC isjayoo. . To fandche icft
of <hc Parts of this Triangle. . -, .
Firft, To find thc< Angle C, • it is the
Complement of the other two Angles to 180 -,
for the three Angles always toakc iZo dtg.
is in the third Rule : So that thcfe two An-
gles, A being 30 iieg. and B 45 fg^ing ai-
ded together, ,nlake 7 5 deg. and their Gom-
plementto iSobeing 105^4. « the Angle
^'se'condly. The Angles being all thi^
khown, the $ides unknown may be found
by their Proportion to their oppofite Angles,
as before i for the Proportion holds alfo m
theft. Thus to find the Side A C ,
AtthtSineof the Angle h 30 d. 9.^9^22
\ to the Side ofpofed to it CB 2900. 3»4<^i3|S
SotbeSi«eoftbeJHgle^^'id. ^M94»5
__ Sum of fecond and third 13,311883
theoPPvptt Side A C 4101 35*"?.'3
In
Uj {JbltqHe I riangUfi 7 1
,. In fad) Cafes as thefei when you have a
^ine ^t Tangent in tbe iifft place; you roay
work, by the Arnhmeijcd Complement
thereof^ ind (b favc the'Subtradiiop, as [
ihewed ehap. II* And To Khali do in thQ
following Operations.
Thirdl Jr, Then to find the Other Side A B,
"by the oppofitc Aligle at C, which is 105.
Here becaufe the Angle exceeds po Jeg*
you tnuft work by the Complement to 180,
which is 75.
As tbe Sim (jf A 3 o d. AriuComp. 0,3 o 1 03 a
Tb fheSididppffjfi^toitCB ipoo. 3,4<523p8
So the: Sine ofC 105, viz. Shte 7 J. 9^9^p^^
tpthi Side (fpfifidfiB ^662. jt^.y^^S^jz
' Thus have you all the Parts of the Triangle.
Prop^tfo.,
Tti^ Sides md an An^ i^pfofedto one of tbem
bring given J t$ find the other Anglei and
the ihhd SUe*
This is but the Converfc of the former »
for the Sides and Angles have a mutual pro-
portion one to th$ other,,
'^Mmpk. 'In the Tiiangle ABC, fig*^*
let the Sides given be AC4iorr and CB
liffbOy whereunto the Angk oppofcd i^ A 30
3# to And the Angle B.
As
7* Of Oblique Triangles.
Ai the Sidt A B 2900 Cmf^ At. 4y $3^60%
to the Sine ef the cff. Ang. A 30 rf. 9^69%9^o
So the Side A C 4101 3 612896
^0 the Sine ef the offofiti Ang.B ^9,849452
tpbicb it ^^ dig*
* Now the Angks A being 30^. and E 45
d. which make 75, the Angle C muft be
105 d* the Cempkment'to 1 80, and the Side
oppolcd thereto 5602^ as was found before*
Prop. 61.
i$po Sides ef an Obtufte irisngle^ m$b dfe
Angle contained betv^een tbem^ being given
\ to find the other An^lej and Side*
• In the Triangle A C D, tig. 4. let the
^ide AC be 4101, and the Side A 05602^
and* the Angle between them at A 30 ^ and
it is required to iind the othef 1W9 Angles,
and the Side CD*
To refolve this ObliqueTrtangle,'f;is a good
plain way to part it into two Right-angled
Triangles, by letting fiill the i^rpendicatar
C B from the Angle C To perform whicb»
Firft, For the Right Aqgle A BC, you
have the Hypotfienufal AC ^lou ^nd the
Angle at A 30 deg. Therefore as in Propofi-
iion 55. by the Rule of oppofite Prbpor tioD^ <
As
Of Oblique TriangUs. 75
So A 30 <fcg. *# C B 2051.
Andagain,
JjB^odeg. #0 A C 4101 :
S0C6€nleg.toA.B^^^x,
Thos you have all the. Sides and Anglei of
the one of thcfe Triangles A C B. . '' '^
isCBD, fubttadthcSide AB. which was
?,^?i*%?,'^' .*"? *^"' y°" have the two
ftraight Sides of the T.iangle CBD^phs,
C B 205 1, and B D 205 1 : And fo you nTav.
as m Pw^ 57. find the Angle D by Tan!
gents* ■"''"..
Laftly Forthc Side CD, .^opprfJte
Froportibn, . _ . ' ^ "^ '
-**Bx:,;«oP454:j WB^oi.?,cb ai»oi.
Ta»e theSuro pi the twq/^ifc A D 5^02
^fchetni and woxk thus. S . ^ ,« j^^
' ' This
7^ . KJj KJtf^iqw: jLricmi^$^i*
t'his added to half the Angles un- JL m.
known, fhcws* the greater An- 75 o
gleto be 105 ieg.zrid fubtrafted 30 o
from it, fhcws the let Angle to j J^ ^
be 45 dtg* o m* " —
. And thus havifi^ all the Angles, +5 ®
jfoa niay find the anknown Side C D by its
oppoGtc Angle at A-
Prop. 62*
paving thi three Sides of an Oiliqui Trhngh^
to find tbeAngUs* ,
In the Triangle A C D, Fig. 4; Sup{>o(^
the greater Side A Dbc ^602
The two Icffer C AC 4101.
• Side^ ^ Z CDy^poo
The Sum of xhde ti*o 7001
The Difference of them 1201
Jit the greaiift SHe - * jftfea c(?.^iJ>2^ 1 d^
Ho Sum of the liegh - /f^oi 3,845^1^0
Sotbe JXfet^. oftbtm ^ 1201 3^ojp 543
:te d fourth Number i$bi '^3^76^
. vThis 1501 is AE a fiart of the grcateft
Stdc^ which being fubtrai^ed from it, the
Perpendicular will fall in tbe'middk 6f tk
Rcmainer thereo(i and Co part itintd two
Right-angled Tdan|l€^.
« •
Y^dtf
Of PIninTriangtes. jf
^m the greater Side A D beitig jtfos
TJe part ti be JubiraHed A E I sOl
Itbere remains E D ■ - ~ " 4101
3lk i&tf// whereof ' if D 3 » to 2050
which is the' plaVe ivbera . tti€ ^Ptr{>6}diculat
C B falls, and is the Bafe of the kttct Tti-
tngle DBC. And! rbi^ fubtfaded fioih
riie greater Side^ ka&es:355j for cheBaiib (rf*i
the greater Triangle ABC. .
Now having thcfe two Bafds of thcfe two
Triangles, and their Hypotenuias 4104, and
syob given before^ ^0^ niayby theJftiileof
Oppoute Sides to their Aiigles ArA all ^'the
Angfes,-- "- ••- 'i^ t:- * .^
I. Iiitht Triangle AS Q r/I : .
^/AC4ioi, i!k^9odegii - i- »
5^AB355r, $&'C6ddeg. ^^
The €Qnr)pleni€Dt wfaereot 11 the An^ A
joi^g. ■ . '- ". ' • ^ - (
/. fc. Then ifl the Triangle C B D^ . t
>fiCD2pbo, tif^fcxiig., r^ *' ; *
Si^ BP 2050, ti'C45^; ' - ^
iVhofe Compkment is the Ap^e at 1)45 i.
Tl^s in the firft J Triangle' A Ci:),:. we
have found the Aligleat A. to be 30 de^. the
'Aii^gl^ at/D'to be4f^^'aiid the two Aisles
^^t C to J)t Adi^. : antf ^j degi tiiac is 10 13!
xo^degk ' -i • • -. • • .' '" .\ •- ',: t
t
(
s.*
"1 O F
Ji
spherical Triangle
HEte iikewifeyou i:fiay take a few Geoe*
iadilydcsifertbe belter un<krA«mi]iig
thcfc TrUnglcs. * ^
i, I*. ThefeSpheiial Triaagles confift of fix
Paints;,! that 15, thttt Sides ftiid ihree Aiiglcs it
ilLy;ilMree of which • being kooWfli thcn^
may !be fmind out. ^
a. The three Sides of a Spherical. TriaSf
gk ate Parts Of Alches of ilirct GresK Cii-
desof a Spheres andasPlainjTrianglct air
meafured by a Mtafive or Scale of £%ual.
^zjo^ k thefeate to be mcafiired by a Scale
or Arch of Equal Degrees.
5« A&JQreac Circle is. any fuch Circle as
divides the Sphere qr Globe into two equal
Parts » as the EquinqifShlj the tcHpcick^ the
: v4,' irhefvSidtn of iheiSides of a Spherical
iXtiai^ are IcTs t hkn ti^o Stnatcirdc^ji .
ijf^rTha.*Sum 6f.tbf^bree Angles of «
pbtrkial .. T) iaiigkjk aiia greater than ti^
Right Angles, 'but lets than fix.
6, A Spherical Triangle is either Rc<!^a&
luUr, or an Obli(]te- angular Triangle*.
. 7- Th
B
/
2.7 -5 4- C
^^- 8
fO.^ 76. pr^
*
y*
'^..TiieSifiespf the Attigtes ate Proporti(>-'
iialcotfaeSines^of tlkJjr c^p^ilte Sides V ttA
oa tht'cKfokxuf^ the Sin€$ of the Sidet af4
ptop0rcionalcb.theiiopp6(k€ Anglcft >
8; laR^^angledTiUngks, th^Sidtq^
pofite to the Right Aiif^kls trailed the Bam
the other twb ai^ emailed Stdc$ ot Legs« ^ ''
^. ;^A. I^tpendiculac U fwt of an Aitb ^ 4
Great Circle^ which, being Ut fill Cr^m atW
Af^lt of ti TirkiDglev ctits-^ke ofpofite &iak
of the Triangle at Right Angles, and fa par^
(he Obttqoc Trieste into fWo Rigbt-ahgldd
l>ia^les4 PM^tfix^f^VmsiiviaxAW^^
Sidfs o^ ing^9 fb^dBfickd/ rnoft be icm^
tinae fdded '^ether ^^ 4nd loixie times 4)«ip^
tra(^e^ from eaoh othcry ac^ofding ^Siliai
Ferpendic(ila«/ fiills. y^'tdm or vritbout did
.Triang^te* * * / - j
4 «
Of Bkbi'dngied ^fherical TriattgUi,^
rr ?rop. ^3/ Caft t/
In tl^jR^ht^angled Triangle A 6 Q A
teprefents'the Cquinoaial Poiot, A B ^is an
Arch of the EcHptick, accorAng id the Lod^
? ' Fa gitttd«
\
7#, Of Spkaicil Tria^lei^
^todc.of iheScm inibe b^ioDtogoflU^
ftMri>$athat KBis^i^deg. BC (btwsthe*
CkfUoatioaof the' Sufi from the .E<|oiiiodU
al in th#t Loogitudev m4 AG its an Arch;
'^ thiiiEquiDp^Mr GiKle^ (hcwiog At Kight
^^^609 of the Son to B. ^ * : '
Now. knowing AfiLto'be 30^2 an4 die
AagU^ the Eclipcick at A tobct^itL^o^m.
kis Inquired to find the Declination tf the
SiM, that is, . the Side B C ^ppoHee^ to the
Angl<at># A^ i . i
idifhfB^dimorSm^p^d. iq,doQOOo
<2a tbi Bmrf tht" Baft B C 3 d i. f >^^Sp76
•iTa l^J^l^^/ the 'Side B G 1 1 i. 36' ^9»2,pptf 70
which is the DediiYat ioh of th^' Sun tor tha^
^lioint&of the'Etliptiek. ^Andif you take
this Sine of the Angle of the Ecliptiek^ 1 3 i
30 in. which is ^^00,700, and write it down
in a t^aperby itfetf, and lay it to eacK Dt*
^^(^c^.Mimite^ ofjHkC^oa^^ oJ
io a(hl ificm together; writing •ut their Sum
in a littie^opH;; if will^be nof reat tabot to
nr)ake an exa<%Xable,dtewing tnis Da^tinrntiDQ
*^ir\:it& fet^ite «rti Minute of thclEcliptick
-^^: thi^ alfo i«vthr#at of ktting ftff a Pff
pendicular front an unknowp .^^g^c % . foe
^ GH$ ArpcndteijSa^ to A C , fif om the Ao-
"fele:B^" - \:'^ : O 1- ;-. :^. -
i . - ' -., ^ • ••• •• . - • i • . # ^ ■ r, «
V •
'^x.-ia c i Prop
» ,
ing kitm^i io find tieSidt 'adjaUn$ toibj^t
^
^s fbe KadiiUttf^tbeCi^iu if tT^Afi^t h^orpn '.
\^ fbe 7We«t«f <fce,^j4,:io theJoHgeni of
.'^ Thus tji^^B^fc; AB b?ii|B ^hfe ^ngitvl^
* of .the; Sua .^6 ^* ,an J cbc 4f^l^ A-OHciiig ^
^^ iig, 3 o * win . -the Side A C w ill be toiij^
^ Aicepponm j^af Eomt. , , r i^ ; - . t
; .^/ 1^^' Ift^^, or 00 ifcg. I :. . , ' J o.opdoop
Si ibi Tangent of kl&^'pM.^od. 970 14^^
20#l^!rtfif2eifl^AC27iL54mi ^p>72j837
Tkus taKte&jfedl U^^isjr Jf#<i3y *t Y^**
«9.*J «»Hc ^ Tabic of R,i|h\,^#^^^ /or
4vefy Degree of the Strns Longuua«,' as 1)€-
;, l[<^c fox tl^c Decliivtfioft> .^ t ^ v . . vl * iv
\y ..Thw ajfpjs w Jva^^oC-^^k^iiugjfiill • ««-
pendicular from an Angle knovciV Ftt A
.^M<% 6^»^.A£;$mitB:G icbc.fiQe atttther
.J»l Right ^gfe*i6t^^^^ J A
•n » r ••*
F 3 Ptop.
/
Prop. ^5. C»fc 3-
T(h«tlfi and '(Wpf the dhliquji Anfjts..ba%
' iMntmy'id^ilfe liber QHiiueA^^
: unffHf of tUAnghftam^eJt.'
"- thus the Bifc A B bdqg JO *§•' and tfic
Angle kM ^'39^ ^^ A"5^^ ^ ^^^' ^
found ^S>,*^i M >«i/i' <vhiiph Is the A%Ic of
4hat Poid^'OfThe'ecriptkk w4th'jhc Mw-i
■ ' Aba thuiydoli^cillt^e ^l?»es-of tie
Ridit-ineled Tr^ngJ« fif ^Cl''''tlitte lie
iSlRf f «W[?s to find them ^ Iwf thcfe are tj*
Stioft libiSy, ,ha^g Ac Jlidmi'm the fitf
*i^c-v if .-..I.? A ,•.:''.■■• »••..• ■ - : -
4t tht Jia^uti t« the Ct-fint^m tftbe iUa-
I ■ . ' }iEBui*/rf(.: Ja (fie^Ttiott^r- A ft 6, the ^
A C being zftliftf^m^ itfi <&^^e SG bt^
iog H <*• |o «• the Rafi: A ^ mil be ^o <fc|.
. 1
t i P«oi
Of Siifrm^TriMgUf, A^
^wo Sides keing given^ Ufnd f^W tf
. ^ ^ OHiquLAkgku. [ A
^/ ^2^e 5i))re ^tht Side next the Jngh re^redj
istoibeKadm:
So is the TfangHti^^ftbi'OpfiBfiti Side^ to the
ToHgent of the Angle iemdred.
V Thus; irf the Triangle aBC, \tfi? fiidc
A C being 2yd 54 m*'^^ the Side E C be*
lug 1 1 d. ^qnf. the A n|[le A wjll ^ fpupd ,
to be 23 A 30 m/ ^
Hercvrprk by the CQa^)^ ^rirh* fa the
fif ft place. -^ , ^ ^ . "^
TC6 the ^.adius f ,^lo,oobboo
SofbeioHgent ofUC n ^/.'so' 9,^d84t^
' ' ' Prop* i^iB. Cafe tf: "^
Che ef the Sides; and tbr Obti^ Angle nex^
t . « hhg g^^ ^jindtke:^^^*], . -
'A^ibtOf'ftmiaftbe^Jln^t 'gi^',''\ ^ t\
RadiHS : ' '"v. -
< - ^ % ^ ^i
V 1 1 • T
F. A ■ ' '>■/• V. -So
i
N .
t^ Of SpherivdtTi'iangkf.
So the Side k^ C beinpay d. fu nt tnd the
Ande at ^zzd^ joMi^you (hall ftnd t^e
Co/T A, iang^^A C .:»? l^adiuiy tang. A B.
aj (i. 3P a? ^ 54* po^ . joi.^ ^
» • ^
BAjp* ^. '. Qfc 7-
• a
^
X
iht tf fbe.Siderr and $be pbUqn^. Angle. hsxt
Uy bHug'kllim'iiiif.fif^tliu^fher SQe.
As the kadiui^ to the "tarfgent of ^ the Angle
* ff^^ •' ■ ' •
^ the SUie of the Side given^ t§ the T'difgent tf
0f the Side reqtdred. .. ,'.
i;(et-A<;;bc2/rf.54m: \\\t Angle A ij ft
40 f»; the Side C B wiH ,be found x 1 1
Ra^t^j Tsfig. K: iSine^C, tang^CE.- ^
P»e of ttk Sideti sudr the 0&/i^ '^gk *ftxt
-i*i Vftf^i/*? few ^wit'.^j*«' i*iig?e'ifofflr ;
gt the Ci^ntif tbt ^ven Sfdit^ tt'mOifUke^
.^tbe Angle rtqmred. '
"" l^t 4 C i>e 3^ <%. ^4 fMM. fad the, ^q-
f;le A33 ieg, ^omf, the Angk B will be
oaai 6p dtg. 22 uuH. ■■
. fitdmfy Sku. A :.: O/: AC,. Ci^T^. , ^ '
. Prdpr 7y. Cafe p» ^ :"! .
■ ■ ■ - ' »^
0#if ^ f6e Sides and iht AigU opj^ti ii W ^
■f bewg kp^pn^ to find fW BaJ^ •""' *
L(^BCfeer4>^£. SO n4f$* and. the Angle
^ A 2 2 deg. 3 o mw. you will Ani the Bafe A B
/£mA,-S^e3C;V2Up£Kf^5ttfrA^Cf^
• ^J*59 Ji^jo pp. 27.54.
-V
,^72. Cafe la •
^/fie of the Sides and the Angli ofpifid to it hi*
, ijS^^^i^,^ to fifid^ey^^ '}^
CectBClKiM^gSOifrffft and the^oglc
A 23 ^2. 3 o mm. jou will find the Side A C
A t^k^%i^ffiCr*S4dit(StSM^G^'^
23.3QUV Ut4rt -^ , 99.., W-Ht
•i^«
'■V^- iJT^ ■ o^ . o.:j
$4 Of ^k^^ Tw^.
• >
Pfop. 73. .'Cftfc II. ^ ;
Oii0^ Af Sides and iht Angle '^ffofidj^ h
hiinggfveHy iofind tbtdtbct ObUqm Angk*
SuppoTe Br€. u dig^ 5^ mvr« .^nd the An*
aA^ kft^d^gf $Qmin, ihe Ap^e B will he
lodiul Sfi Jig. 2z inin^ \ ' ^ '
Oi-'BG; cVtA : : Hadius Sine^.
' ' 1;- • • ' i. X" ' • ^' ' '
Prop. 74. Cafe 12.
Omtif'tht" -iidis 0Hd^ the t^tMtg \0MW, to
fitU shiVbliqui' MngltMii^ M ike fyn^. Side,
The Sidfo||€iSg:A C 27 rffg,c54 wiir. and
j{)bcJ8»ffA.B^|^.<if^. the An^k A will be
Ijli^. A K, Kadikj : : jTit^.A C, C^^ A.
Prop. 75. ,C»ft:i3* iN
OH^^iidti 'MHd iht Bafeitiag ^n^ ^^
fiid^ Angliofpoftd4it^iSidt^
The Side AC being 27^. 54m. and the
Ba^ A B 30 ^. the Aiiglc at B oppofite 10 the
jlKi4< A C will be found 6pd,t2nh
Smi h^y ILadms:: SintACjiiHtB.
Propb
qfs^i^4:mif^.^ H
•A
•■.
• - - V
.: Prop. 7& iCftft 14, ■■>
One cf the Sides and the Bafe hdug gheii^ u
Jiud ihevtber Side. ^ — -»- — "- t
. Tb<^5jld<j A C beUij3gy/.5,||l^. ^a Die
^alTc kbsod. the Side ec wHl be foiiwl
C<^ A C. Jiaiiiu:': Cop A B, £0^ B C.
Attbe tangent <f me of the 4»gUtt u to the
Cojineojftbe Bafi.'^ ,• :
t trite )«i« a^/ifM ii%Atf irN)rj^'<»'4«l
1^ OfSfSericklmangk^^^^
Shith^ CtfiiuB :i KaJim^ CcfinekC*
■w^^— I p I I I li ft ill '0
.« <
o;.^
OP , . Uj . .. .
*«0F 79. TGafe 17.
tewg gamt ufini tie aide offi^i^-tci- tbe
« V . » %♦ J ► - ^ -^. ^ ^j - ♦ \^ ^ * •> t • «. w
Work by oppofition of Sides airi<i^>En|1e$.
\Aj • tbf^^^ if the At^mifed'iio ibt'^Siie
St ifilk^iHe t'^A»gU efphfidW-tU Side
rtqmred,
to the Sine ^ the SideS^ed^ '
k
tv^J^^w/tfyiftS^ Oolicttb Hie j^tiiiive
To that the Suns Longitude in the beginning
-of iWi^^^^Va^.^l^'t'^dft'^hl^fitfK-
zon: Soyoufhall haW V -f^ftn'iJicYiktfUi^,
Jfc#4£;^^VA.B^to»#AI**?M*creiii '^the^^fttlc
A B i^^VUfl^i ^^Itk 8aD^'3dif^ the
^*^^ « V Angle
/ '\
Angle A is the Angle of the Eelipcick 23 deg.
^omin* the Suns gitatcft. D(clinatioo, the
S^e« B,D and B E if iH lie in the HtuitOfii
and cut tbe^ Equinal3ial in the Foiot O^ i>n
the Eafl (ide, and in the Point ^fir Qp tib? Weft
Side of the Globes and fe BD or BEjft-
pt^nt ^he ^mptirade of the Son/ 'dr^is
Horizontal Diftahce ftom his EqninoQ^it
i^lfing and fetting. ^ laOlf^ the Angles IP
and £ are the Complements of the l^atimde
^ 4<tow therefore In the Trianf^ ABE^^
haVing the Side A3 S<^J^» the Angle ati^
t^dep^pmin* and tbie- Angk at E 3S^/f^«
'y>mmi\ht qdeftioh is, to know the Side,-
4^fi£, i/vhichi^theAhipIitaile. '^ ^c
Work according to the Rule propo&d, you ^
(hallfind^
38.30 3<5*<> . ;?,5t3<>. 'S^i *.
which is the Amplitude of the Sun in the
"Point B> whereunto^: JD ■ is e^ual t!* <)nc
bett)g the Amf>Utude.oiv the E^ fide, ;t^^
other 6m the Wefly and the-PoinC Ck the
Point of Right A<c^fion yaA tietw^ the^
And ti»e Difference «f: Afe^fion is € £ iM
CD, to be added to or fubtrafted himt\k
Right Afceokfibri, actoiding as thtStttr&th
North or South Latitude. r : 1 : ; :
Plop. 80* Ofe i8*
im>StiH^ Mrid Me'Afigh ^ppvfid fo one if
$lMje Sldi,, ikin^ ^imty i9 find the Angle
ij^dfai H me 6tl^ '
; thtfi is bat the Cowmk d the. laft Piro-
^o&ioo, an|d is perfovined by the ' Pvoporti^.
on M^c^n the Sints of oppofite.Si<)es an4
Example In the Triangle A B E^ fig jk
the$^ieABbff)igjb^if. the hnf^tH^d.
3a fljf. and the Side ftJSL t%d*^xm4 the Aa«-
glc Awiiifae.found^3;^.30iii. ...
As Sini 4^ ^^*9 Sfn^ £> ; S0 Sin* E B) #0 Sin. A«
30.0 . 38.50. 1841 . a^fSO
* ( • /« ....
Prop. 81. Caie ip.
1tm4iJk^ ^kd M Angte-tnelkded hH$^m ihent
beitg tijkwai 'ic^find tbtiftber Side, :
. Tq ie(bl?e this i^rppoGtioQ j the befiwaf
b to tetp\rp ((he OUique Triangle a^to two
R|ghc^gk4 Triangles, and then ii¥o^k by
)^ forifvcf RukSf to find either a Side or an
Angls, by any three, parts of the Triangle
which arf. known*
; fr tb« Tria^ngle Z P ®^ Fif^ 7. let Preprt-
ientrthe pole of^t he. World, Z the Zenith of
ImUny o the Place of (be Sun^ having^oft*
of LoBgimdi:. Now in this Triai^ P It
bdsg 3 8 deg. 30 min. \thc Cooiplenfient of the
Laticpde of L9Hdlm% let P <$>be7o JL the
Complement of t^e "Suns DetliMcion, andl
die Angle at P 3 1 JUg. 34 mn. the Difbmci
(kotnthe ^etidian ) the ^ueftion il tb fnd
the Side Z 0, which is the D^fl^ee of fh<
Sun ftom the Zenith, and' 15 the Coibple*
tfieni! of fhbSuns Altitude. ' r
The way 10 ie(blve this, fe 4ktll to let
fait a Perpendicttlav ffotn the Point Z^
upon the Side Pe^ whkh wiH fill in the
Point R. The length of thif Petpendioilac
ZR tnaf be found bjr cbefirflCafe, wd the
Side PR by the Second Ca<ei whidi beif^
Tubtiafted firotn pd, gi^es the Side Jl €> :
lb the Triangle P Z O is divided intci f «ro
Right-angled Triangles, Z F R and 2 K.
14ow having' the two Sides ZR and R.Q^
you may hnd the SM«S ' Z O by this
iour^ Ptd^jpofirion^ whieh^if Vhe tbteg^ de«
-wed* .'.)•'.'■.
But tOttiake this (bmewhit (hotter, and
to do it at two Ope^arionss witnout finding
the length of the Perpendicular Z R^ Iroric
fhiis* * •'* •
Fifft, As tbefLadiMs at Sine tf 1 H p/ ^
' - • So'tbp7ang€mofiVy' \ • • "••'
Ta tk^tanim cfiht Ai\ PR.,> -• :
' . ^ S^condly^
5^a Of .SfBericdl Triable f
TBtkeCofii^rfZV: ,
$0 the Height of the Sua at that diflancib
^om the Meridian will be al)bttt 46 ^. ha^
yingjhat Dedinalion.
By jhis Pf ppeiitioD aUbi having die Com^
plenoeiits of the Latitude of iiny t^o Places^
pif Jr<Mr Ditfef ence of I^ongitude, which is
;fce Angle at P, you may find their Di^
iimcCy Hrhich is th6 Side Z €>•
Lrkewifc haviag the Complements of the
.Latitudes, or Declinations of any two Stars,
and the Difference of their Longitudes or
}ftigbt Afcenfions for the Angle at P, you
oiay find their OifiancCt Which uritl be the
,SJde3t0- ^
.^B^t in letting fall ^this Perpendiculai^
tfometimcs it v^lll fall without the Triangle^
a% here it doth, within thf; Triangle ; lin that
Cafe the Side of the Triangle muft be coo-
Hinued, and fo there will be two Right*
^gled Triai^es» the me included within
itlieipth^r^ . , ^ iv .
. As for inAance, Fig. 8. If the Triangle
ABD were ^en, to, let fall a ^Pcrpcndicit*
lar frofb B, the Perpendicular BC falls
without the Triangle, upon the Side A D
pr^IiKigcd tpCfr^nd^fp the twoi^ight^inglcd
,X^c-'^. ts-^ - \ . * ■ Tiianglct
Of spherical Triatt^ks. ^1
Triangles found hereby ^ill be A C B and
D C B: ' and fq ^ou ii[)ay by the fotooet
Proipoficion^ find out the Side B D. ^
Vtop. 82. Cafe 20.
»
Tiro 5f^f/ im^ t^ /^ir^/^ ikcluiedbwtg fyfftlmi
t$ fiffi tither of tie oiBit Augieu
As in the Tiianglc 2 P O, tig. 7. 1(90#* .
log ZV^BJeg. jowfi^f.and Pq 70<&oiii*
and the Angk fiidtg.^^tnm to find the
Angle at O. . ,,
firft let fall the Peipendicalar 2 R, pr^nd
rhc Arch B R, as in Cafe jg. Thai,
^/ the Sine of O R, to the Sine of PR .-
^ Sa the tang'rf V^to the tang^of G>> 30 ^ 28*
m
Prop. 83. Cafe 2t.
'tn^oSiits hmi givetty and metf Ae AnkUi
neott t9 the Side Unkpemt^ to find that Sidk
As in the Triangle Z F ©, Ftp 7. bavu)g
the Side 2 P 38 deg. 30 mn* and2 ® 4^ dL
oiif« and the Angle at P3I if.34m« tofind
Fiftt by. the Bafe 2 P, and the Angle P^
find cbc Stfe P R being next to the faid An- ^
tie, t>y the fecood Cafe, wbkb wUlbe344.
Q Theii
^ /
^2 i)f Spherical TrUngki.'
Then,
^ AstbeCoftffiZ, f^fheCof.ofVR:
52 min. 30 ftc.
which two parts of the Side added together,
noake (he Sid^^P Q 70 ^
it the ^ Perpendicular fall without the
Triangle, the twd parts (boiild be fubtraded
. fron*tocb other. - - \ -<
' ' >
* m- , '
Ptop. ^4; Cafe 22;
T'rrtf Sides heing given^ arid one of the AngUs
* neiict ibe other Side^ to find the Amgk in-^
eluded . h^tween the tt»o Sides given.
"Bi thc^TCrismgle Z ;P.0, knowing.2 P ^^d.
30 m. and Z 40 V. o w. and the Angle P
31 ^. 34^« tofind the>A4ngkat%.
, JFilithnd the Apgle PZRby,tW thud
Q^^%^ by ;tbe Baf^ i P and the Oblfque An-
gle P, which will be found to ^ Ije #4 ^^.
ip min. Then, '
Mihetangent of Z <S ^y i r ./: . -
T'ofhefangekftflfX?: • ^ /i v^ ^'
Wf ik apmof F rR V >4 Ari^ 1^
r^ *ibf Corme of OZK ^K^ 44''
<n4J — (iJ'
ff^ieh added together mal^ ^ i^^ 03
n^iEM^-jf the wht^^Artgh ^Z,
* 1
Prop.
^^'fMhs and th^SUi i^ienBHng g,Vk
. to find either of the other SideV. ' ' c ^
.8^,'" 1*^^ J'»»i««c Zf -O, having zp"
J- ' I hen, • • * ^^ V y.f* j^T
So ibe ^Hi. of f i, wr*»^; ^ 2^ 0;^ ^, 5--
Prop. %6. Gafea4. " ''^ '^
, g^fH, 10 f4 the itlierAn^u, , . ,• ^
3 /«,» to ^ndthTinglcat O. ' *^'' ^'*'
% O 2 r/ '"• "^ *5 ''• 44 «. for the An.
G t The*
94 Of Sfherical TriangUu
Thdn,
AJ the Sine ef ?ZR, totbeSine^ 6> 2R :
S0 the QfifZ P 0, la $be Cof. ^ Z © P^
Prop. 87. Cafe 25.
TW if n^/e/ /reiff^ 'jgftM, tfir<;f me rf the Sidti
ddjoymtg to tbt Angle MJ^n ftm, t^ find At
SoJk hetwtitn the two Angles given*
As in the Triangle Z P O, having the two
Angks P 9 1 Jeg. ^-nm* and O 30 JU 28 m.
atid the Side Z F38 d* 50 m. Co hnd the Side
PO.
Fifff, by the Bafe PZ and the AD$Ie P
you loay find the Side PR to be 34 ^7 m.
30 fe^ by the fecond PropoGtion of Right-
angled Triangles.
i.if/R, toCof.V;
So tang. P Z, to fang. P R, 34 A7' 30^'
i. AstbeTmtg.ofOy totbeXang.ofVi
So tbe Sine tfVK ^^d* ')m» iCffee.
TotbtSine^QK 35 5a 30
■«*■
l^icfe a p»ti «f <ie7 ^ ^^ ^^.
(-.
Pro|»4
1*
Of Sfherical fri^n^kf, 95
Pfpp.88. Ofe2tf.
im Angle f iiiug given^ and mi of ibe Sides
ntxt tbt Angk mtkiumfy u find fir fiii
Angle.
As in the Tiiangle 2 P O, haf ii^ the An-
glcP ^idf 34111. and the Ang^c O 30 4/.
2^ Iff* and the Side ZP ^%d.^onu Qe» tp
the Angle of Z which is yet unknown, .to
find this Angle.
Firft find the Angle P Z R, by the M<: P
Z, and the Angle ?> as in the third Piopch
fitiopt .
jtsK^toCof.BafeVZi
Sotang.V^y foC9tangfVTLK^6^d.iffn.
Then tind the other part of the Angle
O Z R, and add them together thus. ^
As tkeOfrf P, $0 thiCof 9f Q ;
So ibe Sine of P Z R 6^d. ipm,
^0tkpSine9fQZK ^5 44
«
Jfbicbnidtdma\fVZ^. 130 03
Prop«8^« Cafe 27^
T'^r li&rrr SUes being gji^en^ to find ^hfir rf
the Angles*
In the Triangle P Z O, Jig. 7. having? ?
the Complement of the Elevation of the
G ^ Pole
9^ Of SfhrmlTriuKgUi.
^ole gSi^g. jewriir. and P O the Diflance
of the Sun tronj the Pole 70 dig. and 2
the Coniplec&cnc of the Hdtght /s^odeg* to
iriiA the Angle at P, which is the Surfs Di-*
fijOiccLftcuD the Mhfidian* wbicb reiiqifarcd
into Time, is the Hour of the Day.. ' :
fiilj, fet down jh^ Side oppofed to the
Jjlnglfc dcfii-cd, then fl}e other tv^o Sidds,^ th^n
the Sum -of thq thret Sides, th<?ri tfie half
Sdnnr^ thereof > jaltly, tf^e Diffctcnce between
tfti$*alf- and the firft ;Side. Sb thef will be
Slajped re^dy .for ^ope^apon, accordnia to this
'roportidn. • ' \' ^ .
1; At the'RatRusjoibe Sineof one of the Sides :
So U the Sine of the oth^r Siae^ ti a fourth
Sine. . • '^ '
^. As ihkt foHTtk Shtt^ to the She of half the
SumoftbeS'tdes: ' \ ^ " '
^So Utht Sineof the Viferctfce hetweeif the
half Shih and the Side opfoftd iojhe An-
gtt re/jniredy to a JhenthSine.
•Now if ^ou add the Radius to tHt^ fcvenfh
•gine, and then take, h^ If the Sum thereof, .1
jott-'ihalPhave the Sine* of an Afch^*' whofe |
Complement being doubled, will be the Aq- i
gledefired.'-. ^ ''": , """
ments Arithmeti<3al';of the* two Sinesof th("
§idcs coi^jprehendipgtbc Arjglci. and fain*
Of spherical Triangles. 97
Su^tBs together, the Work is far more ready \
as yon may fee tbe manner of work both
ways in the/oUoWing Example.
Z0 40 o jo.Radius* C^mpl^Aru
PTfc 38- 30 P"7P4i4? o;20585o
P <?> 70 o \9^719%6 *o;o27oi4»
' /SkW I 4S 30 /^p 7^713 5 ; ^zW.
i5ir»i 74715 7^3^380 PI98338 1
A/:Z0 34 15 ^5?^75^J5» P,750558
iSic^. *^^ 4*^ M*;;/. 19,733738 5«;» af ti?^ 4.
Kef' "B^ad. added 19^6660^ }p p666o^
■II » -I ■ —
Half thereof asj^joi i ^,983301
^ fyhichis tbe Sm of fy deg. 47 ww, 13 fee.
* tf /f^ doubled maizes 3 1 ^^g. 3 4 min* 2 ^ /?c#
which is th^ Amgle of the Sxins Diftance from
the Meridian i which, converted iato time,
fliewsthe Hour of the Day.
By chefame manner of yverk you may find
J he Angle at 2, which is the Suns Azimuth
irom the North part of the Meridian, \o be
130 deg.. 3 min. 1 1 fee. or the Angle at
to be 30 deg* 28 i»i/f. 11 fee. ' .
. . Prop.jj^o, Cafe aS.-
gj tbe three Angle ii 'to find any of the three
Sides.
If infiead of the greareft AngJe next the
Side inijuired) yqi) take its Complement to
G 4 ' i%Qdeg^
98 Of Sfheri^d Tria^gUu
i%o deg. thcfc Angles will be turned into
Sides, and the Sid^s into Angles » fo the
Woik will be the (ame as in the forfDcr Pro*
poiition.
As in the Tf iangk Z P 0^ fcnpwipg the An-
gle Z P O to be 3 1 Jkg. 34 min* 26ftciV Z Q
130 dtg. 3 min^ ix ftc. and % P 30 Jki*
a min. 1 1 fee. if it were required to tind the
Side t O bppofite to the Angle Z P 0. fAc
13© i/eg.3 wiif. 1 1 jfc. out of 180 degf tlicrc
teiptins 49 dig* ^6mm^4P fee*
Then as if you had a Triangle of thref
hnown Sides, vi^ one of 3 1 deg. 54 min.
26 fic. another of ^tdeg* 28 mm* ti fee.
and the third of 4^ deg* 5P min. 4^ fee* and,
you wou|d tind trie Aflgfe pppoiitc to the
Jirftof^thefe!bidcs» Set the Work as in the
lafttropofition.
d* ^«f. fie*
59 2<i
34 26 domphAfit^*
28 l7 9,2^4920
5* 49 o,ii6o§4
5>9iS54J>
f he half n^hireof being 9>97^S^5
it the Coftne of 20 deg* which hting doHbte4^
lives the Side detired to be 40 deg. '
Mgle ofppte |£
tcffcr Angle . 30
(>m}hgrea\er _^^
Shmof the^. iil
HiflfSum 55
Pjf. /r«« Jfr/i ?^
59
^5
43
Of spherical Triaftgks. 9^
And lb you may find any of the othet
Sides./
But wbeQ yptt know^ either thre^ Sides
and one Angle, or three Angles and one
Sidet you may iind the other by their oppo^
fite Proportion, as in the fcventecnth and
eigjjtceptb Prbpofitions^
Theie arc all the ufual Calesof TriangleSt
Many Varieties naight be added to eadi Cafc,
and fome Fundamental Axioms, whkh
might more fully^ demonfirate tbefe Pio*
portions) but the l^ook being bpt fiiiail, and
intended more for 'Pradice th^n^ Theory, I
(hall leave you for jthefe things to other Aut
thors.
PRO*
\ >
nop
J
PROPO.SITIQKS
I N
ASTRONOMY.
« . ■ »• "^ « '
TT^Hbughl have partlf applied th* Ex-
J ianripl^s'of ch<J Cafes of Spherical Tri-
t*glc§ to the Refolution of Aftroiwtnical Pro-
portions, Y^^ ^^ ^^ not be amiis toapply
fhe'tn^io Aftronoctiy a little mpre plainly,
and to add Tome common and necefTary Pro-
pofitions#
/ .
Prop. pi.
TCo finithe Suns Declination at any time*
t.Ajtbi Radius, «r Sim^ of fo dcg^ /
2; Sp the Sii^e of the Diftance, or Longitude
of the Sua from the next EgninoQislr
point: ' ,
3* So is the Sine of the Suns greateft Declina-
tion.
^^o^ii>tSine of tht Suns De<#nation in that
^ LoHgittide* ' ^.
Now to make thcfc PropoGcions a little '
(he rcpre praftical and comprchenfive, you •
may
may take notice of this , Rule of Mr. Ought^
red s; how to bring any of f hefe four parrs of
the Operation into the Ufi place ', fo that
if you know any three of tiae pafts/>te^iiti
out the other thereby^ '
The Proportion holds thus between them.
^s firfi^ to fecoftd: So thirds U fmf^ "i* I
As thirds tfffimrtb ^ So jltfi-, tctfti^udi t V *
Asficotid^u fwf^:, Sajmnh^uthM^ .^ '. c
Jjfofisikt *^ tidrd: Si fit^fU,. ta fi^^: >
Thus, As by the Longitude aod gteatcft
Declination Qt.^ ADgle of AiEchptkk!^^
may knovij the prefect iJoclipattdn^V fe i|
'the prefent Declination^ "and the grea^De*
f lination, you may know the Longitude.
Prop, p2.
^9 find the Sum Right ftfHenfion, Br'^dny
uA^tbeKaSm^ . ^ '\'*x
2. 'to the Sine of tbe Compliment of th Suns
gEcatcft V Decrmatio'n : - ^ ^
^. So the langtnt of the Longittf<Jc''bf the
$\xn,ft(mAc:um'EqtAm!iiaUf&int^ ' - <.
±.1o the 'iangm af'#*e Right Afcenfipn of
Prop.
SC9 JjirMomieal Prfff§fitions.
*
%$ fM ih &in% Afcenfional DilTercocC) v
^ sity ef ibefc*
|. As ibi Radios,
%• to the l^ngim rf tkt Poles Heigirt ;
|« Sotket^mt if the Suns Declination,
4* Til ibr Shu 4 ^ ^^^ Aicenfional Difle*
tcnce.
llj/hiA added ro^ or fubtfaAed from the
Houf of Sixt ihcws the Suns Rifing and
Spttin^
Prop. P4.
^9 find libit Sun.^ AnnpUtude, ' or ixny of
tbeji.
!• Jf tbe Sine CompUmm of tbo Poles
Height,
2» to ibe Sine ^fBm^imotm-of Ac Suns great^
fft Pecliaation :
3« So tbe Sine cf tbe Suns Longitude from
tbe mxo Eftmaid'poiHt^
4f 7# tbe Sine ef tbf Suns Amplitude ; -
Prop.
tofui the Suns Hoiary DJfiance fiom ifce
Meridian whtil he is due Eaft ot Wc(^ ^
»Hy if theft,
1. A t&f tanim of the Polcsliddi^i
2. Is to the filadius :^
3, So tbelaagM •/ tibe Suns Declination,
4.^* /^^J^Mc «f 4Ar ^uns Homy J3Manee
C4f fioia(beMeiidian,being)ufi£aftc»^cfi.
to find the Altitude of the Sun beios tuA
Eifloi Weft, cr any tftbtji.
I. As the Shu if the Poles Height,
S. 1/ ta tibe Radius : ' , . i
^. So the Shu <f tibe Subs Declination,
4. Tir ^ Spit of the Suns Hei^ beit« ioft
.Eaft or Weft. -'^
Prop.^,
Itojiud ^U Suns Altitude at the Hoar of $^
t* AstbtttAAlvst
S'TethtSiiKeftbef^i^Uii^:
3' S 9 the Sine ^ the Sons Declination,
i'toAeShu^the Son»Heidit tt tfaelibttt
of Silt • , s
T(6 fil fhe Suns Azimuth at tfee Houi pf .SiiJi .
1. ^x^fce Radius,
2. Ta theCtft}t^^l ibtlVoUs Height: ;
;^. So tloi^diigmt cf tht Suns DecUna<ioa, . ..
4-Ta l&? 5r4Hgfl«<^'VSq»s Azimuth /rw
Rdp. 5>J>-
Vay.
r ' r. i : ' . , J • 'i • 'J- *f. '-v^ : -
-rf/ ^itf Radius, ^\ •.;{.'; i^l ,
f(^U^^m i!^r^iE«iStins:xHa^Me frknvtht
flour of Six, ' ^ ' .
'to the tangettt of an Atch^
Which being fubtraiSted ovtf of the Sans Di-
ftsyftct fr6mthe Pole,^ Work again ibus» .
ii^nheX:0ftHe hf^tbe Arch founds ' ' \ •
*2a tbt Cofmt of the nmainm^ ^^ 4f ***
. Suns Diiiapcif«Jl^fkff4^ :^ . v / A . -
Soil tbt.^$4if ihisEo(€4 ffeigbt^ :y /.\^ .,
fSrfkJhsf:.MnHi4l^t^^^ Mpifr
required. "^ .i iJ.
(
. * Prop, ico*
I'd find^ the Hour rf tbt Vay by the Hei^bt^tf
• ^ • fbe Sun. ''
the *Cl6mpfementof^thc^LamW(? tf/ tbl
PI ace J ajid the Complement of the pect?-^
«jlw» pf ibe SUn^ ix\A add thefe'^9^ne'
SidesVbgefher, ^s CjJ(S ^7.^ i/" 5;>*crM|f»^-
anglfsV iind ^find the . Piffcrcncc be^Aicoi
tlieirhatf^umandthe $6ris Altitude. Thcd
worktW. ; '- ^"'^'-'^ '^ :^^^/;-'
1. As tbe Raditi^^ to the Cofine of the Latttuit:
''So tbt Siut of tbe'^unt Vtjlante/r^th
. ' . Pule^ to a fourth Sine. .^ '*. > ^ ,
2 . As t%di fourth Simy U ibt Sim of%ilftb$
Suw* . . , . '!^ .
' ** So tbt^tk of tBc'Viferehcif io dfcVeUb
Cm • t \V.
Vnto ^bich if you add the Kadi^, half that
Sum mil be $be Siner of an Arch^ whofe Comr'
flement being doubled^ mV be the Vtjianee .ef
^tbt '!SMn' jr^^m the Meridian j xpbich' 'iik"
' verUd: into Xtme-, ivifl jbeiv th^ Hour <^ tit
Vay. . • ^^'•
The Operation you mJy fee in Cafe 27, «f
Sfhffrical triangles.
'" ■ Prop.
1 07 AjlrcMlhiid Pir&fophm.
i
\
I
Prop. 10 f. •
7# ftni the AximmJi by tbi Sum Heiglbi.
. Tike the Complcmenc of the Suns De-
> ^Itiiation, the Coinplemehc of fhe Lati-
tudC) arid the Compfemtnt of the'Sun.«
height, and add tnefe three ^ides toj^er
f^Kr, and^ /ind their t5ifference betviretri
their, half Suni, ahd the Suns D'iAance from
the Pole, as in Caft%j* only put the Suns
bitfance from the Pole firft. Then work
thus.
1. 4s ibe Kadm^ to tht Cofikf nf ibt Laii"
iude :
S^tlbi C(ftH€<f tie, Suki Htigbi^ u j fMittU
Sme* ^
^v 4s thai fohfth Sintj to tke Sine of half ibe
Sum:
« 5^ tbi $we of tbe Viferencej to u fevattB
Sine.
.tinto which if yoii add the Radius, hatf
that Sum will be the Sine of an Arch, whofe
'Cocnplement being doubted, ii the ^zi-
niuch dcGred;
A^0if0mi€td Prcpofiiims. 107
Jiaii$igiht AjUghof tbt Azimuthyto find thi'
Bmt-i 9r by the Hskri^ find tki Azitrmlb %
wanyof tbeftTtrms. '
■ •
' . ■ . • ■
I* Ai the Sine Qn^i^^^ 0/ ^bt Sum £)edi«
Dacion, ^
a. 1^ the Sine nf the buns Azimuth : •
S'So th Sm CompUment of ibe Sutis Hdg|ht^
4* 7^0 the Sine 9f ibe Suns Hotaty Vifimctjtqm
^ the Meridian*
' .Pl-op.iaj.
Having the JJniitnde and LafUudecfa^y Staf^
to find the iigbt Ajienfiin and Declmatim
tbtreofi , '
t^Altbt RadiUi^
' io the Sine of Stains tMgihtde ftmibe nexi
EqninoSial tolni :
So tbt Cotangent ef the St^s Latitndiy
20 the 'tangent ef a fotirtB Arch.
Compare tbis fouitfa Arch with tht |brch
of DUiance betweea the Poles of the World
and the Ecliptick, 23 deg. 30 mn. 1 and if
the Latitude and Longitude of jthe Star be
both of one qoalUyy that is, when the Star
hath North jUtitudc in the fix Northern
H. Signs^
Signs T >!f US SlWl^ or South Latitude,
in the fix Southcr|i Sigftf to^ n t 'VOPorK,
fjl^n'fti^l lilCy1Wffe^Wce'Ntwe€^^^jtM»foo^^
Ajtfefcb. ^ ikt \J?ift^ficeof the FqI^s ^^g.
30 min. be your fifth ^f^h. . , t > -^vt, \i
But if the. Longitude ^nJ Latitude of
tHedfar^^bc :Df corilfrafy Qisialittes^ thskf is^
one Northern and the Other Soutfe«J:h,' then
add, this fodrcH'Aich'to the DMtoiiccf- of th«
Poles 2^ rft^." 3 d wifef. and thcK Ston th^t of
ffiatf beyouf fifth Arch y - if^itfr which |iro#'
ceced., • *
> , ■
2. As the Sine of ibtfornik'^rch^
'to the Sine of the fifttf Arch :
:-^^ihe l-aHgef^ of fbeSfar$ Eoffgimis
- rPi'^e taugekt of the Stars TCigh^Afitn-
fioH from the next EquinoSOal Points'
J . As the Cofine of the fourth A^ % • i ' •
^ So the Sine of the Stii¥Lkk9iiei;< '* \ - 1
' f
dsfflfly, for i^odf ef 'ydat '■ WdA, 1
- ' Th'fh^ofiHt'of ibiSfatimiht -y^fi^ilfiJk-t'
■ " ' ;^(r«iE;^ to^^e of iBt J)ectiprdtioii^ - • ' « ^ - ^
'-^^ ^* And
AJirMomieAl Propoftians^ K>gi
And thusjiaving found the Right Afcen-
fion and Kcltnatiori'bf any Star, you may
by the Jtwxf^ fittkf 4pi^kr^^
its DifKiM^crdr iift^TiflDn*^
frotti the Meiidian rjiu any Height crf)fci-
ved, and fo the Jfloui o£ the Night theic-
byv rV\airVf g St& #thc <ifncie^xof rti
t€> 4he «4uthv h^ *iWi
fccnfion from the Right Al^enfioa l)f the
« •
'; M^vVi v.«.; ',.,1: '\o "\vxV i "U tvVi I't
* \ t r •' % fl» •< ..».,' ,. ,- ,vt 1 ».*• (• ... tit ^\ • \.
.;i.-:
U
; p*^' ,;;.
' r*
> r
% « 1 1 • • d.
)• «
« • . . ^<
7 J l'» '>^ ll
» 1
• \
» I
i^ ■
H;.»H...j ,.,,, Met
• •J* ' u« ' '/
'.'iu.i'Xi v'\
\t ' ■ ?»
I< •<.
1 •.•1^:4
♦y^
v;
..V'V/i'.y.'b V \»\ \\i<'>. '*i lO"' r^
• i
•*. \
1 <• .«
^f\^<_. v'-v \'
V . 1^
»■ "
X -I •■
?' TiT il.K
PROPOSinONS
IN
GEOGRAiPHY.
* * • .
'•.'in' •• t
\
Pf op. 104.
jT? find ihf Vlflance of any Mo Unlaces wbM
aiff^er only in l^ikudii being both upon the
fame hkridiau*
U If the two Plices arc upon the fame
fic^e of the tquinojftial : SubttaQ the lejfer
Latitude mt of the ffeme^y the "Rgmai^cT k
tbe Vifiance required.
2* If the one Place been the ooe Gdcdf
the Equinodtal,^ and the other on the other :
jid£the tm LatitUktet together ^ and the Sum is
the JXftance rehired.
Prop. 1 05.
2a l^Hoi» the Viflakce of any ttpo Flaces v^bith
- Mffet only in JLmgitude»
2 • If the Places arc both of them under tMf
Equinodial » S^btraQ the leffer Longitude om
of fbe greater^ tb$ Kemainm k the VijUnce.
2. If
GicgrdphicM ^Prap^ofiions. Hi
" «*l?tK'c twa-Plirtesht^ethcf?tne-Litr-
' Wde,*^ afidib^ under x{t(;<mk Parallel, thcft, •
yii the Kadiuf, ' , ^\ \ <^'^^' '* ; ■ . " : ' "'• ;''*-'
"totheO^ftnetfihtirtatiHidez '; •-
So the SweofJfalftbtifpiffereneecfX^^
, io the Sine if half ibtir D^inde. - ^ / ' • ' *
Prop.*iotf. ^
- ^V- i
. ^ Who)^ Qoc Place T& uimcf tfe Equipoaial,
9aa the omqc, toward ^nha ot tqe rolcs» ^
^s the Ka4bif^ ^ ;^ . . i 2 ^^ . > * •
7i tbe^ofine of jbdr i0lsiffi^
7^9 tb^ CqpHe of mir J)iJtaMi^. r -. mT
'X/^/hcn lK)tb Pjatips aire jt^Qwards one of t6c
:i>pics-: FkA, : • ^: ;;;
AsjbtKadm^ J .;
T£oyBo Cojme (ftbHr D^emice of tongihute :
So the Effiaftgent of the lejjir Lathudi^
'L 2*i fbi tangent rf a fonrtb Arch.
H 8 which
ntiuft be your fifth Arch, ThqJ^•^^^^ -^ , ^' ^
At the CofiHt <f fi^M^:^f^. , «?{o '^-V. ' V
So the Stne of the'leJTer LataHde, ^\, .,
and the otl^j|««a»4ddii«\Saui^j;plc.0.it>fiiifi,
\Astbt Radius 1,
io ti»m^iif^i)flf^k»fW^ :
So the '^o*''»ge»^of/^ l^LatiMdtSt
XU^etatmHtorAfimrthJrcb. , .
c*fiffie^m»^d:'o2ft^3!fle6tht^:La,
in*lner is the rifth Asch. Then ' "■!" * ,
So
to
fiance of apy two Stars, iCvftU ,knovK, their
ccnfion and Declinationj wMoTIl of^g^d
ufe.in.^/friwjwy. ^_ , iv.iSsL^i r.*i^^
* •'.
*t3
' » 4 » V i ^f ■
1 * •m * "l
)}
or'-?".
' ,1 I J . » » <
" I
.ft
« *
n-'A'Y-iQ-&t-iCi^U.
i*
mO*4
«i »-» »* V
ful n}w» yet jpfirfi6a;^q(^, iij^ciupijf ^ca-
,aiep;h^^, need M^ . gop^; sHil ip jd^'k ^'
lomc fort 9«cdwjil8f ^qv^uip« good ^i|L^
and Circular Sailjiipg^,o«:Si^i^,b|,dipiV^Jl
> t
If 4 PfaJH Sailing
MitcS) each Minute or Mile containing about
doooFeet. . >
In this ArttHe Seaman hath the(e helps.
Fh(i, He hath bis Compafs co dircdl him
which way hegQes* which is divided iirftinto
efoux Cardinal loinH or Quartern, Eaft, VVcfl, :
North, South , and each df thcfe Quartets
are divided into cij^ht c<yid\ parts, connmonly
caMcd RunrA)5/ pi^l^irtg in ill 3 vPoim^. So
^that^'ftfeertiig tjr iheCpnipafs <vcB inade and
'^dtrf jr riidHfied,* the Sisa-|nan always i^nows
"H^hith way hcfiits, tq a^vcry frtiaft nr^atter,
Irhe fecond help ihie Sea-mah hath in keep-
ing Ms Accoupt^ isa cireful Obfervatmil (,bV
'thV L6g-lirie, 61^ ■ ifenc. other gobd'tWty^ hoW
'^itif Mtfe or IVaiu^ he:fails evefv Hour,
*tjtffcf6^ei7Wkchrana every Day; -/:^'
.Thrairtdihapi? the 1inoi;yledg ktt»pBK>.
^atibrf of the tatimde, bftthSr the f lace
*cfttf #hei)ee he fails; and whcti? he is' arri-
^t*^, ^ WHiM'he iVW fill/. •''• '^^V • •'•
And Qi^toCthttfe three (hbfe^ t* the po^
<9fr^6f ^f iaiti' ^nitt^ei,^1ic5)<^ td%rtoir
Hfl Willis het^ffctsf'for rHe teb^g of his
^^myi fe^Hk^fie W^rtofeany tirftc
^ftc^Vic j?, few^ ei* h* hath^ filled,; aifd
WraV^hi^ /^niJ^^^hicH^^iiray, pr
V^fi^m^t^ Tf^^t^ of ^ thr,tothria^^ ^Hc; is to
W «|Kt-lifnta KeaingttlA tim^sl
ifyih Kiimk, and $ke t^^mce finlii ffert^iv,
la f»d the D^knme ^ hammde*
y ,
. ISxampk. In the fitft Figwre 6f Plain Tri^
angles. Let C A;by the.MeTidian Um, C B
the Rutob-linefialedupcNa, lidog;^ueh-
Weftcily 6* Nottl^Eafteily frctn the Mui-
thereon be C A j 50 Miles : ■. The Qfic^^a is
toM the EKAeirdMre of iLatituite^ .whi<j)
isfhirkogthof the Uffi^C A ioth«LT>!iatigJe
' H^r wdtking by -t^e Sule of tlMi'PiiQ|>or'
'tiet^^ifSdii is bctmta opppfite. Sidbi and
Angles. ■'' - .■.: .--.. .■,...■.•/ ■j:.jj;.-:i.
^/ the AngU A, tA^ Ufod.pr HaMm,
T» the 4j>pofue Side, C^»j «r VifiaKCf palU
Sttht'^Ajtgte ^ f bdng &« CoOfi: ntC fbe
Rumb Qt AiiglcMQ;>.£Hir^« S«<&.^ m
^9 the Side offffite tbertmta, Pfbkb «i C A
fcr the pifl^a^^oC tathiulc. . .:,,,,,
*•••'-■• l -.;{ ' '.»-'. r- • ,
,i;f.'j 'I
, i!i»(toBi5fce>iJBJ2fipM«te%.;!;i 5::), t.ii *»
^r the Difference of Longitude. .3 a ;
-io<P9ltKlekwis(rl9ce(fpiV^6:VQW/i|4y^eep
iais A«faaBtfh£iiou»i3j»y3c! h9'¥;;^«*^J'<»»
, f4U Eaft 01 Weft,' North 01 South, .:.;f%u;i
; I k.'iu (■ ■* c
In the firft Figure, let C bft*b«rAnele^of
. to know the i^mtmSim^Wf^ a ' J • [
to the T>iffereHce of Latitude C A ; ,
'S^i^ ^»g^e kpo dig. or Kaditit
I'o 1 he Vifiance failed CH-
felr, when your Latitude by Obkffpt^^l^tlg^
jJOfiagrge n^itl\ ^M>M^f Re^^ f^«fi^iPikpft by .
Xl^Uu4f ^cifoup^ tfi be i9iWf\€ltllef$>liMibyRll
,p(;th(:.i^^miH)..; r : A^«» 1 flCCprM^gJlftj^ts
fiyifPiy'9}>',#fttv(B<iLjititj}rff,.jiwi fiwsoiwfft
your Acbountoit,P(3a4|#/ijf^MSfr;.-l 3f!i sIm
ui ^■^»S^Sgf&'#€^ te-,"'*<,:^pi »fee
' Rnwfc /erftfi«^ from one FldMopeWf^
In the firfi figure. Let the <««*lwf«y
C and B, . let C A^tft.j|iaq«ffe^S§S^,»9f,|,%<i-
.Diffetctice of Long\t«4f^j^ilKyi^ftR^i-
Aj the V^ereace of Latitude (fj^'^^if^* ai^tn
r# the Wtrtnct 4 ^^mSli4li ^^<9^9AZ \K
SetbeRadiuff o,30»
which is four Rumbs 3 quaitc^r$</tr« kona ttt^
Ji.-ilT • ^ Meridiii^
/\
ift Pkin Sailing.
Um^ti Somh-^wtfierlyi thae ?s, almod
• Hieie arethefneft common and ti^otfl&ry
llQtesUn Plain SaiHug, which is qnlfm be
ufcdm finallDtfttMcs, ncarihc Equrno^aL
Whete^he Degrees t>f Lonjgifudc are juft e<jaal
it the Dcgfec!f of Latitude, vi;?^ each ofthoB
>«>:MUe5orMiniite§. ; But if ybuarc fardi*
rftawtViom the Equ^titkjialvt^e thdujgh theft
'Ru*il hold good to'find the Difference of La-
^-tfesjbsfnd Drftaricc *^ the-RunbW yet t^ey
^^i1'tniic!iincheLon|ihide^ and thcfefbtcto
'^fini tbi Difference 6f Longitude, you muft,
ufe thcfoiletwing <*fdp6fftiom - ^^ ^•'^ ^'' '
AftbeRadiuty w whole Sine of go di^^ -
^d de'MUtt c&HtdhiidiK m V^j^m if, Lan-
'-'^mde^ifitbiiiLatHkdi. ^^''V^'T- --
Tli68i»the;Liftitude of iibT/^^^^^
make a D^ree«^ •'-"' '«*'-'- ' .' ''^ :' ' /
S9 Of. ^ilei.io S^^ytt^y -l'-'^ -
• '^'- • -' '5CbO'^ •t' i: ^"'- *^ : "^ '':t .> > . .
^ 1 . THcfc
PldiH Sailing. 149
Thefe things niay be done veiy mtM by* the
Table of Natural Sines in the Sta-^ims Ka^
-Thus if ki the fptaiet £an)ple ypur De- ,
parti^f e from the Meridkifi was 280 Miles i'
this divided by tf o, and fo reduced into De*
greesand Minutes of Longitude, und^' the
Equlnodial it yields 4 /i^g. ^omit^ Bill if'
this i2 80 Miles ef Eaft or Weft, orDepaitwe
from the Meridian, Ibouldbein the latitude
of i^0€%. where 30 Milesinake a Degree of
Longitude, divide this 280 Miles by^o, fo^
it yields j> dtg^^oi ^^ fj 'which is 20 min. for
the Difference of Longitude in that Latitude.
But this being fo ncceffary.a ConcIufJon \n'
NaVigatidn, takelt inaixotbcr Form and Eit^
ainple, whtoh will fully explain it, and yield
a nxjierea^ywiy for your Calculation- of tix
Longitude in any Latitude.
r ' Prop. ira.
TBfy iU milts rf Rafting or W^big (tbasifi
- yDHflkfarture from the Mttidian) to find
. arjre 7)ignej and Miwtet of Longitnde an*
fxPtrame tlktennio in any Latitude.
As the Cofm of tVe Latitnde (in a paraHfel
Courfe, or of the twiddle Latitude in any
other* Courfc which hath Diiferenceof
• Latihide,; ^^^''' '
Is
SAtf^MU0i-^^Vtf/kimre:Js0»i tie 1^ :
lo the Miftutes of Longitude m that Latit^m \
L^Cblc the. owrPlii«;:& rile otheif ^Supp^feY
Qjotbs io the. Lacbti4e o£ SP'^dej^^ha .th€:
ii«ui jtibeDepar i urr IrctfH i^hei Mten^ )aip pf <C tOr
i^'iif^yfiKie; of. LMgicade- bet\^e0.thiifetw0
; To'lkcfelve thii, yob cnuft;rieuhe;ri;0ckQR
thefe Mites of Dc^tt»rev.&8o». jf^,(h» Lsad-
ffjddjq Latiwdc^ctwt^'* the twiyf^\^cs^ ib»4
i^ in^ ihic Lritifbdt :of 4S d^i$m^^V^wv§iK
As Cof ^Zyd. 1 $. ComphAritb^ 0,17^^03
?£> 42'd i Jwiii* (jf" Longimde \zp:;6i^';^t
' This yields 4^6 to"». ^' of Lorigft\jfdc»which
divided by 60^ fieUsyd. 6 m. * for the Dif-
i^i«iH:ie of Long^udeat^ thefatworl^lfices^
v> Aad* tbus by lb?, Dirfqf^nce qf .^^dtudc
4^ pfpai tute ftoQi {be.Meridi^n, ^you ipay
keep a nue Accouat by Longitude Md Lati^
* ~ ' * fudc>
" t
ally (feij^, Map, Ji^cfirflng To A^^rwroi^rPdf^
^iaces^as^amen life to di FircaR Nqcj
Youiaay Wof^this;^iro hyNatuirXl Si^*.
/ Tii j Ti. j'l-ji I I- I -ft
' *
•I
\ . . ' ] , ~ ■ , ■
' / • • -5 ' i *
HEre it will be neceffary to have a Tabled
Met^dional ParM, which I hkvedr|wh!
out ot Mt. Wfri^J&i'sl Tables, « td c?erj^ tdnth
Minute of *LatitMdc, accountiwg it m fiibglei
K^.iles or Minutefe of thc'Equinodial, fbcbet-i
tct to, av6id Fra(^ionS) as he and MuNeri^c^d
havedefigncdirj n ■ ? t .
J
*mm
A Tabic of Metidionil Milc^.
the MhMis 4 ^^^ Vegne.
o' I lo ^ '20 I 30 f 40 I 56
•4^:
2%e hkridimdl MUeu
I
o
I
3
4
5
.7
8
9
10
[I
\%
t4
5
J7
18
1^9
10
!,I
H
XZQ
x8o
140
10
' 70
130
190
156
30
90
150
170
40
xro
5.«/
iiol
170
>9o
I CI
of
300
481
?4i
310
37©
43«
491
3*0
380
441
501
^6z
3io
39^
451
57i
340
400
582I
410
471
53^
59*
^03
7M
78^
848
613
*74
73T
797
85?
5i^
684
74<
807
B69
^33
^94
751;
817
879
«43
704
76f
8^7
%%9
<5 3
715
775
838
900}
9(0
.97*
1035
Tl(!»l
983
1045
1108
Ii7i
93 »
993
I181
941
IQ34
1 1 19
119;
1614
X077
1 1 40
Ii0 3f
1014
-10^7
l£14
fcft *■
12.15
»*35
l%^6
^»57
1*67
1178
II89
1199
131a
i3ir
1331
134*
»353
13^4
»371
138^
139^
X407
1418
14x9
1440
1451
1461
^475
1484
»499
I5©5
I 151*
1517
153*
i7
I $49
156J
157*
M^3
1594
160$
1^16
1^1^
i<^38
1^49
l66\
U7X
U83
i^p<i
»7oi
X717
1718
1738
1 75 1
I76i
1773
1785^
179^
1808
i8J9
i8?o
i«4i
185^
I8<fi?
18^7
O I *Q \ go I jO I" 49 I $9
titrUiMd
«M«P>iWi
■^ ^
ll
3»
i3
34
2099
iiyij 1.1S31 xt95
Ifil
10 J 1
!5'
39 i
4«
41
4*
45
4$
4»
14
57
5«
5JL.
»*44
»4f»
*f4«
■ ■ ■* »<
*9*3l 1^34
^^o7
j^4
*I47
tup
1781
ji*3
*x5^
1530
'»^35'
*7J4
^7^r
>87#
i^6H
1341
Mi7
»4^3
»t7o
>35f
Z430
25^3
>*9J
43f7
»44i
XJI9
%^96
*305|
»455
*f3»
i7i«
»P7}
>?4l
1^04
19*7
*^7f
*7f4
^J3S
i7^«
i«4^
1931
3030
311-5
3%oi
3381
3«>44|
313©
3AI7
33**^
33^7^
3050
3*44
3131
33«
34X1
3P7t
315^
5247
333^
34»8
3oaiJ 3015 1 M4
3^^3
3»^i
335J
34*43
3101
3i^.l
3>7^
33^^
345^
3474
35^8
3^^ 5
37*3
39^4
34^^
36ai
37«o
3«ai
3505
3^00
3<?7
57*7
5^ii
3,^1^
3714
3814
^^99\ 3^i<^
3537
3^32
373C>
3«3o
I 3933
3553
3^4^
3747
3847
39SO
4«>T4
41^^
i*d
2122
39»5
4«ai
4»9i* 43«;5
44*8
4003
4110
433 ^
44^
4*38
4351
44^8
403^1 .40S«
414^ 41^4
4*57
43TO
T
^*75
isltijm
J
4
4
5
i
«
3
I
7
8:
"<r
«4'
6r
1
A Table of Meirtdional Miks/
7%e MintOtf rf\ tacb Vegr^i*
e f io I 20 I 20 I 40 I <o
• ^ ' f-*- — n — .- — - ' I
ihe^Merfdhnal Miles*
^alm
'45M
4^43
;4775
♦ 4905
5039
45471 45^7
4<57d
A79^
49^7
4«^t
•481^
4P^9
fcS5
458»
471 1
48 3P
497I'
yio8
46011 4^29
473^1 4754
'4994
48 «3
i5©J7
n<5
5^79
51*4
•5474
^1*
201
11
5103
5J48
5^58
V79n 58t?
521^
.5^75
55«^
5«5
<OII
'5»fo|
531^
55fi
5712
<879
{
5175
5 29y
»4
5**3
5449
*5
5^78
^5404
26
5739
15767
17
^908
' 5^37
i8
70
7*'
M
59^6
5996
6115
6055
6085
6115
6146
6177
6208
1
6139
6271
6303
.<^335
6368
6401
'6414
6468
6foi
'6535
6570
^60^
^640
^«?75
6718
'6747
6783
«JS20
68^7
68^5
^9?3
75
77^
78
79
I
6^971
7211
7469
774^
8048
70I0
7153
7513
7795
8100
70^0
7>95
755^
7844
8i<4
7«89
7338
7605
7^P4
8x-^9
7 1 JO
738^
7^1
794A
3 2*4
Si
n
84
7170
8377
8435
1 8495
8555
$6 16
^t78
874^
S806
t%7%
8^39
'9«07
9077
9-148
pill
9195
9371
5>449
' 9^»8
91^0^
^691
9778
9865
9914
1004^
10141
10238
10338
I10441
to547
106^6
^5
87
9<
10770
1^539
1 25 21
Y39ie
t6ti?
10887
11686
I27I8
14111
TT0017
X455C
17726
^
11133
11999
»29i7 131^0
M9I4
ri.^^3
13388
15311
1IJ98
11344
13^44
*5783
zz6^
manner, '■'■'-'■ - '
Pf6p. lij.
Kftohnkg ihe Latimdirof 4Hy two Pfacis\ u
fMiheM^ididdi 'Ma of MinHilsh-
* • « <
iUvl C: ' J
rirlt, fFben one FUce U W^ffi <W\ EjP^-
Totes >^ Tbcii the Meridional Minutes an-
• _ *• "J.
fwcrable to that Place wh\(fh ^^th I^ti-j
tude^ ^s to be r€ckone4 for the Mcf iqionaj .
tfiffereiice of Latitude, or the Latitiidfe in- ^
largcd.
Secondly, Wbm^ J^otb Places are uwatds
S^e of the fa/e/j ^TThen fubtraft thp Mcri-
tdh'al'Minuti^s anfWeirog to the kffer Lati^
tlfride^ out^of ihb- Meridional -Minutes be-
longing to the greater Latitude^ the' ^etnai«
iieji, :W^11 be tb^. Meridional* MiR^^s;re»
Thirdly, If one Place bave^ North Lati^
inde^ and the otbtr^,^(a^h%K^^ th^ Meridi*
onal Mi|iut« WcJpging. to each f^lace fogc*r
thejr,. ahdtfc Sufii Aeicof is the Mcfi^ioaa*
I 1 ^ HaVmg
i9€i S^ib^ h MercatorV Cb»L
Having thus found out thdc Nfa^toi)^
Miaatei foi any twol^laces) ypu*i^th0
make uft of tbenu.
Prop. li^.
J^ the LMghude and L^uJk cf im§ tiaaiy'
. Ufind thi Bjitmh fhm $be mu totk^pflw*
Firft find the Meridional Miitut^ between
the two. Latitudes V then> .
As thi h&riimat Minmes con$dnti Btfmuti
nntiit •'' ••';.- ^
Sob the t,aim$, ; , - ^
'\.. ';,■; ' Prep, t If.- -' v;: ^
Bjf ti^ T^eren^ 4 taUtHd^j and tie Jiwitti
yen have failed t^m^tQ ptitkfi P^exmc
0f lAn^itttde* V ^\
Fkftfin^the MetidioinalMimtte^ {^loilg;^
ing to the DifCerence of Latitude ^ thet^ ^
As ilhtliadiMy
To thttoHgaH^f thitLnmh
S»4beli/kridmMl Mmmts of Latitude^ ^
To tbeimi tSsida rf hoHgimdiy wbkh yO«
may 4ivide by 4o^ and fo turn ifito^Degrees.
^ . Thcfc
Sailing fyMeratot'i Chart, ia^
Thcfc are the two chief JPipEqfitions
wherein this Table is uftful, viz. To ^nd
the tnie Rumb vai EditeQce bttw^cq -apy
IWof^aces, which in OiiiLll Diftances mar«
perfomiea bytlscRi^cs of Plain Saifldigi as
before. (hewed i efp«c^]]y if ypumaV&piic
6f Prep. 112, fox the' fiodioft of fli^ toijgi-*
"tude, which is fomwh?t ipoic re
fernScd thereby, iu" cjfting u^ y
Reckpiiing every diy or two. I
TAle ii only nccelTjry t'p find the 1
.uifiaticp and LongUpJe of P)ai
nanti'biattfic 107, 10% and lOp
tions, which, miift btufed in thij rfijiiirii^rjjt'
^Satliilg,;aiid alfoare/he mofl ncccffiwy ^fdr
the keeping o( an Account, mult altfr^sj^
wrought by the true Dinerence of Latltu^fi
)ind,riot'by the MeridiiMiiO Table, '.' '
I.Hught,'m»ke niahy Various <^cBio(is
ajidEjjwnplesouf ofthtTc JUlesi but thcfc
^c as Wifuy as are pf ncceflaiy and brdp-
paty ufe*. sod by which- ^l othors may^
^cifoijiied,. , ,■■',,-■.
Is ,^' '.'"^
iii
m
OJptcHtar Sdili*ii^\pr SaifinQji fif
Arch' ofaGreaf Circljs- ^j'hyin-
"is' though in (krtie ;f(:n(c if is thV^iioft
exa&'wiypf Siill'rtg, Ihtwirig ipe ricai,-
i diRiticc'^tivtecD any tvvo^Placf;; i
very diife£iilt,',and witlial pf..]i^llc
eatnen^p^ (elpotn )teep ttieirCourje
Arch, blii'i^c'eicheir drawn afiifc
fonje' CT)0vctiicntes'of''Wjr}l?an3
is In ftitirtgSi. (he ^cS-Jii'dfis, they
tiidrekcrtHe-Sdi^KwifffiiJreirefhey
frdmMXoiirre by 'iipH^mdSy
!)fiti6n'''tif^'"ftiintf 'Htai-Unds oi
So (h^t^tHe?r fc^ ' Vaf i|'.?p. keep
thcif Aaount by thl* farmer Kulcs:" Qnty
'fiaMQkilt fcofiii^'^ ;they tnSy'fil^Waf jltis
'■ttijJijrtimes rhfc -n^aW* way tfc'l^avc the
■feiiftiB''-aBdl6'r^il'%dfe Nortfitt^v.^as m
-rai^irtg home ittxh-M'ftrt]i-Miiif'^^K\i
makes thofe that keep not a trlit Account
by the foimei Rules, but reckon altofjether
by the Plain Chait, to be at the Lands-end
many Leagues before their Account. Alfo
in a Parallel Couife , as ftorri the Landi-
■^.'Ktd to Uw-fptiid'landy you may fee how
yoii may advantage your felvcs by laifing
and
Of Ciradar Sailing. laf
afid clepreffing the Pole lo ox 12 Degrees,
which will be a jgreat help for the keep-
ing .your Account, and yet go a nearer
way than if yoa (houl4 fail on the Parallel
of Eaft and Weft.
Bun beic^u^ this tniy be niore ifeadily
and i^amly performed by Gedmetfy, I
(hall refer you (qt this . to my Ceometrieal
Seaman^ being lately inlarged, and made
inorc prs^ioal^ for tjie rjady keying of
^tmt Account' by rLjititude>na j[.ODgij[u^e,
y flew' Tables for that purp6(e«
•
1
\ l:-.t ^
V
•>-
•
i
•
t
•
- •*
vjm r.)
1 A «
f
it ,
1
t'.uVs
• ■
•,'.- •. .. 'jM
•■{ .
u4:
; ::- (V
^
ttO^
■ »tl-t
- * c rv"^'
r
■ f.
1
'M/yi»J '.w\i
X
IV.
r
1 :tr •
\ •
• *..i\ jc.t
\
►A.
;■• ^'^ tl /
•
^A..
•n.
4
'? ,''? '•'.'
»■ T
1
J
)
1 »
i
«l> '
V
•'
: * ^ ^
• Tn-V.
■ w *
■• '.*
• '
4
•
» "
•
• •
• ■:, ',
J
?3«>
/
J
^■..
4
L: ./•" i • • d F * '- '
^
/
prop, ii^,
T^o mtafme a B$^d hting a long Square*
Firfl meafure the breadth of the Boarc) ia
Inches. Then, ' " -
iif/ia Jnebes or one Fodt in he^^l^i
59 ibt Inches ^ the ' hreddfby
To theLtebijof the ten^tb for (me foot.
V work by the backward Rule. ' _
»^: \*4si%y to li : 5o 6^ to 34.
/ \ Or el(e divide 144, the Inches iasi Foot
of Boards by the Inches of the breadth of
t^a^Board. ^ r -
Soi^ divided }y ^IndnS', fi$ew$ i%Jncbet
' nta)^ a Foot. '
Atid 144 diwded by f yields 16 Inches in oi*
I Of Me^hg^'&c. fgi
\^pd 1 44 divfded by i% yklds % Inches in
Foot. \ ' ,
" So by opening the Cooipaffcs to this di-
'' ihrtce,' and tinning theqfi all >loi% tQ the
Jthd df Hhe Board, j ou may fcnow ho^ ilMiny
r.Jtet life in length. ^
< •
4notber wcq.
' -trt Y*)at Rulet lie divided into Fert, txA
: ■ tSeckhah of Fcer -feftidd of Indies ^ kid
intafott the^Jciigth and- fef eafJth of the Board
I fherti^idt, and mdU?|f>ly the biJe'bjrthc
I other. • ' '•■■^^• *^ ;'' -" '' ''':'"
/ Example.^ A Board U i Foot 17 farts
hread^ and 1 6 Fs^. 3 2 ,p^j longy it eontaim
i^ Fmt.andj^ tenth fart of a Foot almfft, yii»
; ^^cmi: \ '.: :; ^ ^ ;'■ •; .^
I ' • -
• , ■ *■ » 'f ■ • ■
, "^ which 18 lb Foot every way, containing ico
tMi kjM pNf'' vS ftwi u^ foris: tioady i;om
Divide loeby 1 ^« 2 5, «tke JVpdgdbw^fl
hetf. 154*, that 15, 6 Feet 154 parts.
Prop.
Ija Of MeafitrJftg :
Pjrop.'iiS. '
. 2$ partly and phf Utigtb of the JBfr^n is
47 Foot^ Ibip many S quarts af Tiliftg^ paik
Double the length' (that you may count
jboth ^idfs of the Rqpf >; ijtrmakjss p4f cct »
j«[iiiS^ (Jjvi^cd ^Ijy i9o,.,yiel(i i < ,%uares 27
Feet. and ;in halC ' ov^r, which U a littlf
above a quarter 01 a Squaie^ ^^.
> «
In'Paving men reckon by the Yar| Square;
(b each Yard bath p fquare Feet. " * '
-4 tffrf^i/f Co»n or^ T^djbafy ^7 Feet 3 5 parts
jn brta4tby^nd[^o Foot 5 parts in ImQb >
^" ' iiop^ mani S quart Tdrdsdith it cdntiin f
Multiply 17. 35 by 30. 5, the Produ<a,wirt
liei;29. X75ii*vrfaj4i^f)^ h^ f^ thtQup?
cient will be 58^7971, f9me!Vl^arab^<e< 5$
%ZM^ j^yqulrtcfS. - <L .1 1
Propt
offd Sfirifep^. tjgf
■•»•!» V / «
r - Prop. ISO.' '^
t I ■■•
. Tn meafming of Land, a Perch or Pok is
1 6 Feet and 2^ half» andfouv Poles in brp9<i^|
and 4CV11? kngth R)ake*ai)c^Aa,e r |b tdat aa
Acre is iVo Polcf .
Now to mcafyre ^a Awe piece of Land,
multijpJjgonQ of $hc SicU5,^)^y t)if otbeiSidc
jbyning fo it, aird divide the fumTjySi^o.^ *
4 piedeQf'L09fd^heiffg:4Xi!Pita one myl^hnd
'., %o ffiltjiramtbfi^ miy^tl^fimkitiplkdhmiif
As idoiitt^ikt m'B Side^)P\4tr.iy:'' r .;ri^;«;^
Prop. 121. J
and tKe Perpendicular from the As^g^ coo-
led to that long Side, and then multiply the
half of the onej^;tli[0r^ole of the other,
Let we side be 66 j^ tie ftrpeneicmar 40 »
r mbpckM^Ai. by i $o^^ j^di , 7 Atra md ak
half fiO" tbt Cmtenu.
* t34 Of Meafifthig
Or clfe you may multiply the Side 60 ^nd
thcPcrpcndiculat ipcogctficr^ they make
a400> arid divide it by j^o^whofe Log.
V is 2.505150) whidi ii the double of one
Acfti it yields the fatbe Coneeift.
Jf^zo^ l#idd: 5^40, ^4^%o^
^ Prop. i3t*
TV MeafitTB $ trapezia^ or i douhU trUngk.
, .^ ,,;
. Mttltiply both the Berpendiiiilars by half
^ CKagonal Lii\e, ^'rhich ^ i$ the con^mon
B^epf both the Tmbgles^and divide fc^ i6q.
ibm k% At tUsg^HsU'-line he dt^, ^ # the
Ferpendictdafsx^rik€0Urii mfiti^sdAd
^iA» nuiks Z^\ 9bk% multifBed iyMfthe
ViagonaUllm ao, mdki ^Sa h ,v^kt ^tivUkd
kyi60i mJkls 2 Acresy ^R^ds zo Foles.
Or ellc, .: ^L .
lart a J : ' .
4fi ibt hng^ if AtVi^intsUthn ^(i>y to tie
^ t^iamt. '- • • • ' •';■■' -^ '•'.
re,', ..." . ♦ • , > • * ' ' :> 1 * ' ' '
. »^ *
Multiply half th« Dtamet^t % half the
Cifioaaiteiencp^ and divide the l^odu^ by
« Sik. the IHatmitf $/ rin Circlt hthig 140
toU$^ and the Grcukfl^rtmt 4^0 fUts h tbe
bdf 9/ ibefi Mo^ being 220 and ^o, nndii^
fUtd iogetber^ ^ftfAil^ 154^ Folei'^ ubUh
Svidedky u66^ ykU 96 Jhfti and a qnarter*
Orelfe, multiply the Diameter being 14a y
in it feif, it makes i^tfoot which divided
by 205.7 (whofe Logattthqa is 2,5089 }i>^
ftiakes 9 6 Act cs 2 2 partSi^
2*fLj>g.(5f 140 t,i4tfi2&
Donhkd miiks$ ^^29^2%4
Subfir. 203. 7, Log* j^3o8py i
lk/fX«t5»^aa« i.f8j2#^
. . ' - •
Prop. 124.
Let the Oval be $0 fdk$ one way, tn4l
40 Poles the other, What is the Content >
Kfoltiply the length 40 by the breadth 36^
It ffiakesi^oo; which divide by 2O3 f-.^
dtyieMs 9 Acres, 3 Roods^ 33 Perches.
Prop. i2S»
By this Number 203 xi you ma^ atfc^
fM the Aacs contained Iti Jiiiy half Circle^
ofq^aurter* orjSxtKpart/oranyfadiSedioti
of a Chrcte, fvmUiplyiog ilhe Setnidiatneteir'
by
-^9
*^ Of Meajkriffg t.
che Compafs^inQ, and dxfidingby 203 ,:
•"•♦,1 ' ii'*''' >)' *
f Brkk,-woik; If "^^siily n?eafuted .by .thc:
^od/ciColCjjC^i^jHQd containing ad foot
and an half) and a'^rlckrw^ll pf, one Brick'
and, tn h^lf thick bting 6nc. Rod fquare, \i
acieunted for a Rod of Brick- W9rk 9 and
if^do Bricks will makcfach a Rod of
Wotk. .
iaoi*^ . thefc Walls or Sxiti, df ttoufes
niuft be firft meafHred according to their
fetiti in length and breadth, according to
Art, thereby .to find out how many Rods
they contain i and bccaufe a Rod is {lich a
|bitigii)cafuriQf^< 11 f^ittdobcft, as in oieafur^ng
of Laiid^ to dividt the Rod into 10 parts^
and jTo each btf th^m into iQleiTer parts,
imkingjn all lOo parts, or 1000 if you will i
and thuf me^fcoriog the length ?|id br(adthi
(orrathei the height) of any Wall, and mul-
tiplying them together, you (hall have the
Content in Rods, and iooor looQ parts of
I' Rod.
Example.. ' ., ,^
]^ Lit 4 ft^au about an Orchard $r Garaen he
4oiti9ds in hngihy and half atiod high%
' ' thai
and Survey iM. 13*7-
fist a 50 parts 0/ the tidd bigbi Hem many
MultiflUd by the breadtb^ Tiods 00 . j3
•- ■■■ m
% «
7ieldsTi0di 30 00
i- Again, the Wall of an Bonfe bting thru
Jiodi bigh^ 03 CO
jtndi^,R9diiHtompaft^ . 12 00
Mnltiplifd makfs Rods 36 00
Bi^c now all Walls arc iiot of this thickncCi;
fomearc two Bricks, fpme three : To reduce
Rods of fiich f hicknefs to Rods of ordinary
IWofkof one Brick and an half thick, work
thus, \
j4j tbe thickiiefs of sn ordinary Kod ofTFarkl
reckfned in half Brul^j^ iphkb is j ^
^0 she tbiel(nifi of any other ifaU in balf^
Sricki » viz. two Bric^j and an balfS 5
mhich, makss 5» or any other tbickitefiy J
So the ' number of Kods of tbe Content^
found by meafwe^ 5
^0 the Kods which it will yield of ordinary ?
. Wor^ of a Bricks and an half tbicl^ 3 ^ ,
Or for your more plain and ready ufe take
this Table.
A Table
. '. "N
f3^
Of MeafiriMg
ATabk co recluce a Brich-wattbt aiiy
^1 thichnefs to the Comciitof Ordimry
Work) which is a Brick aiKi an half
Akk
Jbttbickitefsflf the fTaB, Btkt^^
^^— ♦•■•p^r"
I .1 li I 2 I *i I 3 I Ji 1 . 4
M
Ibt Content thtr eofr educed im Rods anifm$4
-
:« *T3
8L III- a'
K Sly* r?
? ?(! ?1^ 2»lf -1-^
X
X
a
4
5
61
1 33
h DO
} 33i
I 00
3 oo
4 oo
5 po
I 331
4 6j
1 33
^ en
I
3
T
IE
8
67
3?
<^7
33
6
.7
9
SO
4 <^P
4 ^^7
5 33
^ CO
d CO
7 ©J
.8 00
9 o^
^ ^7lio oo
8 ool
9 33
10 67
IX QO
«3 33
10 oo
X oo
4 CO
6 eo
i^ oo
^o oo
ii C01
II 61 1.4 00
»3 35
(5 CO
l6 61
16 00
\S 00
M3
4^7
7 CO
II 61
__• ' '
1 4 06
i^ 3 J
1^7
r33
I0i»7
I^TOQ
l»^7 tM3
SI QQ
>o oojij 3311^^7
14-00.
II
11
13
4
7 33
8 00
9 33
1 1 oo|i4 ^r)iS 33
<t 00 i^ ooiio 60
13 <^^i7 33
14 ct
usjio o6\i% Oo
18 ^7
&o o
'3 33
2.5 00
xt 00
14 00
x< 00
2.1 6j\%6 00
,8 00
3x57
30 oo|35co
»i^3*
3o?3b#^7
3735
40 op
itftio 6i\i$^oo
17 n 33 I7 00
18 00
I^' CO
%i 33
11 ^7
14 CO
»5 33
fc^ 67
x8 }3
30 00
31 <7
lo .co{zi» ^7h3 Im^ ^^
3* 0^137 33
34. oc 3^^7
3^ CO 41 60
38 0^3
44 31
4^*7
4*^7
4533
4860
5067
53 33
n <
\
and l&trveyift£. i^$
Prop. 127.
^o'tHeaJkre'a fleet of Tmhtr txaBly ppan..
The ufual w^y is to have a Line upon thdt
Ruler^ io (he* how roasy Incheis ipakc a
Foot tor any Square. But it is as goccf a
way, or better Cefpecially if you cafi it up
with 76Ur Pen") to know hour miach t)nc
> Foot length of any Square >will yield in pro^;
portion to a Foot of Timber, which is to
cbntain 1718 Cubicle Inches i which yoa
may^o by this Rule;
If tht Squdteofiz Incba, ffbicbk 14^
far every Fm Itngtb yield one Fpotofi^ ^
timbit^ or tarts . J. ^^^
fFbat JhaB any other Squitre^ (H tbe^ .^
, Square of i^wbicbii y ^
Itbt Anfti^er mS be o, 2 50
No\y multiply thii by theiAicnbet of Feec
in length) and it yields the Content of the
jD^iccc of Timber in Feet and part.^ > Js if
il!u fieoe of timber 6 Incbes SqHare^jn>ere 10
Foot loHg^ it tvoHld contMu 2 Foot $^O^ti^
§raH hulf
And thns you may draw out a. T^foy
your inorejjeady ufe^ as ytfu. ihay fee^ tnf
fuTch^4^i fatitm
14* Of Mei^fitring
yt&p^ 12%.
lU meafmri •ny kjnd if timber j ^mgj^ h bi
net fquare > btit rf any firm^ , a§ fbref^
fiuare^ fimt f quart', many fqu^re^ rHmd^
0» of any other faJUeii\ fuvided it hi
firsiiii and equal aU almg*
Oft up the Supeificial Content at the
end thenof, and find how many Inches it
contains by tho Geomctsical Pfopofitions be^
toreirgoing, for the finding the Content of
the Triangle, loog^Squte, manf-SqnatCt
rofiid Circle, ##• and then wdik afi before
in tbe laA.
As 14^ the inches of the Suftrfieiiik Cinwel
- ff e^end or Side of aCuhiek, f^^
ToaCukicl^^ Foot, conHkomg I090 farfst .
Sa -Ao Snferfidal Omten^ of tbo end of amy
fkci of timhr^ iu it bo 100, aoo, 300
Indks^
"Xtfh Solid Contim if m0 Footlongtb ibertef^
Sojisafhli 6nA for 100 Inches Contene,
^i ^4fa|ts ) for 4fcOo Inches, the doubta
thereof, 1,3$]^') for 300, 3,08}, that is,
a Foioi o^ parts V whidi you may eaii!y
ttakeimo {jiiah aT^bk as thiafor your uQu
^W Slurv^mg.
»4
A Tabfc AcWing the Solid Costcut c
one Foot length of an; piece of Txwba
iccofding to the $ui»ettici«l Copttec a
the end thereof.
1
4(
i
2
3
4
6
?
o
o
o
007
014
021
028
o 035
o 042
2 Z^ <>49
So 056
069
208
2.78
r® 347
60 o 417
i»A
, 166 6 <5o4
I?
* f t-i
^ go6®
20Q00
irifrl
I
20 «j3
27 :f78
48 71 1
62 .500
4
,8
iJU
•■*
14^ Of Meajiiying
- Prop* 1 2.9»
^ Mdre eafie way for vnufHring found imb,cr*
; Bccaufe ibtre i» fo much abufc in the cnea-
furing ef tound Tigober, I (hall (bevr you
fomwhaca more ^tain and ready way for Riea*^
fuiing of round Timber, which is only thus.
; Take the compafs thereof with a ftring^and
ihen meafuring the firing by your Ruler, fee
^ow many Inches the Tree i$ in Compafs,, and
then find thofe Inches in the Table, and there
^ou (ball fee how ma^y Inches and parts of
that Tree will make a Foot of Timber^which
talce out with your QompaiTes, and turn thccn
over from one end tt) the other of the Tree»
the fcveral fpaces will (hew how many Feet of
Timber is in that Tree.
TifiJ tit the compafi of a ' Tree, be 60 Inches \
you Jhafl find i the 7Me againji 60 Inch* ^nr*
^apy thafSlMcko^far.ofanlHcbjdividediHto
j I OD farfs^ mgkgs a ^Foot tfTtimber ^ fo ib4t if
\ihi fioii of Umbtr he it Foot loHj^y then k
*V€ry nesf±^ foot of Ijmbir in it h for^ I2 foot
idnd i iHtbkfometpbaimore tbaii 34 Foot. .
f If the Tree exceed thccompafs 6f 160 Inc.
f which is thegreatcft numbaV in the Table J
^hentake half the compafs^and Hhd the number,*
^iruhc Table belonging thereutito, Sirtd divicle
if by 4. » that iSjtake a quarter of that ntimber %
"* r«ndidm^$Jnches.a&ii^^
oHCimbei of a Tree^^f that compafs* /
and Surveying.
UJ
A fiblc Ihewing bow many Inchn in length mokd
a Foot of Timber, of any Tree or rwind picc^
of Timbtt *
hole CodipaTsii kDOM.
P6^:\mb:far.
|c.»Ml.,.j«.| i f»f.|i«(,,V|
117 IJ
4'
U 91
7J
4 3^
II
'J?. 46
41
'? >'
71
4 1"
. ii
1,5 80
4}
It 74
73
-, 0!
>J
I.J „
44
11 4> .
74
f 97
><
no 79
4
10 .71
7!
3. 8.
15
?* 3i
10 ,1*
■ -7*
» 74
'i6
!, !i
.9 »J
77
J H
'7
■7! 1,
9 4»
' 78
J U
d '«
i1 0.
9' 04
' 5 79
j-:<(
■S'?
S-, I j
8 <,
■S «o
3' 39
^.0
!♦ >s
S 81
* li
3 }'
S "
« >J
,». »3
,58.
3 '3
4* 8<
7- 73
a "i
3 i»
!i
40- po
7 *i
ft 84
t.o*
jr «s
■7- 11
^ '7
;J 01
-a 'I
'34 74
<: >'
* it
« 94
1'
i'. 1*
< (is
•s-*
,». »7
»> 79
«. 4!
*.»»
1 8d
V-«
*7 76
« >4
S'!
' '3
e-i,
ij-e.
< 0,
|-,o
£ £8
j!»
>4 I!
.,. 8,
>5 J,i
1 tfi
«?;
i* ((0
!. <(
^^«r-
1 ,37
II n
,S -47
S SS
I 51
;i
19 91
'5 3®
94
,. 4«
H
U 7I
5. '4
91
I 41
31
^i7.74
.4 SI
»<
» 3«
.,*
'i/(.:il<i
•4 84
" !|7
I 31
■ 3!
■(• 8«
4 "
>'.
* H
!*
IJ 04
4 !<
9?
1 »i
3»
".< .1
.
4 43
■ ^06
,^ " 17
"^
Kj
Prop.
Maoy times Timber k Icfler at one €n4
than t^e otbcx, tod moft Trees or roiindl
lrimt>eir is fa.' JJow the coinrooii waj( tQ
meafurie fucb ^ piece of Tjimb^r, js to meafurq
it by the fquaie pr comps^fs t^keo in the mid^
die c{ierebf : buf thar gives the qu^ntitjf k
'goo4 de^l too little \ ana tbe p)ore tapering
pt is, ft) mnch the woifc
Tliefe pieces of tapering "^ipiber are eitbf |
p^rti of Con^s pr Py ra<Did«s« No w the miy
to noe^fure a whole Coficov Py ramide is aiin
,trof. 43, ^.tq muUipIyd^efvp^rBcialCopT
<^t ot t|iejP9(e by a thirds part) of the kogtb^
And tne beA and plaineft Mf^y to mesrfuf^
thefe S|ed*rons, Will be« a^'yQU may fire in vn
turch^ersfi^iterHi SfntOr^tid the I^n^thof
thic wljioje f yramide Of Cpnc, aqd Q> tt? &t4
the coptciu thereof) tjien by the fupepr^aj
Contept at thq kff&t eiH) , apd the ipnffU
Whichibelongs ^ that pai;t^ fiqd th^ CQOtent
therfofi as if it wetie ?: goi^ OV Py lafnji^ of
"itfelf.: tamy, Subfr^a thf Qofitent of thi>
Jefler tJQp-paift ftom thqOontentofthe Whole^
the Rqniainef muft needs he <he Cqnte^t of
thebigge^r bottofopirc^wttfch yoR wn^ t^
• jimalutc. . ■ ' '' ■ ''' '• •' : /
■
V$w u find the hngth rf thi tofrpari cf tbe
Com prtyramdf pbieh kentcif*
Mearuie the Sides or Diameters of thf
two ends, and obfiivehow much thef dtfftr
from each other in breadth Then,
^/ tb$ DifferiHci ^ the hcoAb tf tke Ifr^ t»d/f
TofbeliHgthbihftenfbtm: '
So tbe breadth of the greater tndy
%o tbe tpboh length of tbe Cme or fyrsmide* ^
Or if tMs nuiy feem diSicult and tedious,
yott taiay part your piece of Timbef as it
were into feveral pacts; irp or $ Fopt Idng,
and fo meafure each f»aft aecordbg td itf
fquare 01 compafs in the fiiidd1e» a^d theq
add thetn all together.- Thfe wH! come itx^
near \ aftd yon will Htwl much difiereDce bc^
tween this, and meafa^ing the. whok pi^
Ittoncebymemidtdle. ^
• * • ■*
• - ■- . ; I • J ,
I
^ ' * *
- • - • • . . . J
Ii4 OF
14^
« \
■***"T TTT-T TT"
^\
« • . «
)., ..y - . J .
li r
eAUGING,
Tt^lffrc b not ^uch difference between
,'*... p4«gWg an^nM?a(uiit\g ojlicr Solids 'i
pnlv (h^ejivare mea^jf^^by Feet .ajpdpaits,
t^ie yeffclsi>y pajlopf,jQuarts> and Pints.
L:t Tl^^Jf ®*^ twp-j^jyg^hcjfcin chiefly neccf-
t?/jj yet both.;;<}9nir9Vf;itc<I. Firft, Thcfc
ypfli^^^bfjnglQr^^ n^oft paxt of irregulair
^%">??i" how tO;H4»^i^hcm to a rcguJai
^ppojtioo^ .;§e<;oiid^y^,to ftpd .the true
quarttity of tne Gallon in Cubick Inches, ox
parts of a Foot. ' ''
For the firft of thcfc, one of the beft ways
is that of Mr, Oughtbrei^ Mcafure the Di-
ameter of the Cask both at the Bung andae
t he H€ad, -a^ % tlietc DiaineteTs4ind out
the Area of' their Circles. Then take two
thirds' of the Area at the Bung, and one
third of the Area at the Head, and add thein
fcg«hcr>-^is M^U-^te the mean Area of the
VcffcK Lafl^y, If you piultiply thi$ roca«
Area by the length of the Vcffel, it will
(hew
Of Gauging. 147
lhew<how many folid Inches theVcfltt coq<*
tstinsv ci/hich if you divide by the Nurobcv
of folid Inches in one Gallon, ic will (hemr
you how many Gallons the Cask will hold. .
E^amplf . Supfofe a Wint Cash^. having the
JDiameter at the H^ad t^ Lfcbes y sna the
T)iamiter at the Buftg ^2 Inches \ and the
lepgtb ^ Inches^ Ifhat U the Content ? '
f of the jfrea at the Head is 84,823
I of the Area of the I mg are ^ jtf^idtf
TChe Sum •( thefe tvpo 620^^%^
MtiUiplUd: by the length _40
Makis folid Inches 2483^)5^0
which divided by, the fpUd Inches in one Gallon
qf Wine, tphicb are 231 Jnchesj yiefds^fer
the content 107 Gallons ^o f^rtSy tb^jd^
'fomii^ai above half a Gofhn.^
But now hqx is (he fecond di(Ecu}fy to
TcfolTC iiow many folid Inches are in aGal-
lonj .^ ' ^ ' :
' * A^ foir the Wine Gallon, it hath befen and
ftill iscomcncniy received, that a Wine 6aK
Ion contains 23 1 Cubick Inches : yet Dr. Wy^ \
bardpW^ds that it is fomwhat leG)m;.224
or 22 5 at mod. But this diflfercnce is not fo
much as others malce it in the Ale Gallon >
i^r though moft old Gaugets and the Coopers
make the Ale Gallon to the Wine Gallon as '
4 to 5 ) fo that the Wine Gallon being 23 1
Inches,
»#» Of Gaging.
Indiei, thcAIeHGtlldmis^aSSbdifS^; yet
fiflce the Excife ie is accounted by them but
Sla Cqbick Inches.
. According to thefe IKules and ObCet vttioiis
tbU TTable is calcul^ed^ (hewing the f of the
Aieaatthe Hisad, and , of the Area at the
oungi of any Cask ready caft up in Gallons
aod lOCQ^paits for Wine noeafiii^i (o that
mafunng the Dianaetec of any Cask at the
Hcf^ and at the Bung, and adding thefo
two Numbers together, and multiplyhig
rhe^ Suna by the length of the Cask, you
(hall find the Content thereof in Vl^oeGgl*
Example. Snffwfi ^ Vmmmy
Akiht Head fe l^it Incbef ^^3^
Jltihtmgubt 32 tiubis ^>;2i
thiSnmifibefitm • 1 df8f
Mulf^lUd by the teHgfh ^p htebes 40
MM^s vity mar m before 107,^^
that if, 107 GJhns 520 far$s tf a Gafmi
tif4i H^ aUtik ahfU m half of a GdHofi.
1
A Tabic ^ the Gaugjog of winc
1
■1
3
4
5
6
7
8
I' 9
I
o
o
o
9
o
p
I
o
Q
«3
o
P
■ -
i8
3o|
o
o
o
o
o
p
b
o
col
oio
'o\Z
071.
f37
0(
o
o
o
o
p
o
o
o
M5
!.
4CX9
Joo
74?/
8
9
o
:r
9i^3^«
0^0 1 z.
o
o
9
I
I
I
i
I
I
cp^
III
183
^7A
583
44ti
5 ^^
7314
8i9
906
000
09if7
*94^
,30k
^9<^
7771
5©^
C4<>
3»
3J
34
*34'i
I
I
i
I
f
5*
37
3«
3?
4t
4l
4>^i
1
4?
44
4#
47
4I
4f
50
14
ij]3
54
5!
57
53
3
1
i
310
38»
4^9
7M
ti3
f34
coo
1^4
>95
19H
54>4
^33
063
lU
554
48i
S13
5?45
080
3
3
3
3
3
4
4
\
i
4
f
f
f
7
7
7
7
8
1
4^8
tT<
93^
»P^
171
44^
^15
809
CCQ
3^
79f
ca7
44*
85K
l»9
81^5
108
5^4
^H
%fo
Toufnaviiil|fgetfa5i5T!*|>Ie td parfcjof ijjciiqs. and draw It
Ak ©a!toi», as you may feeat large in my r^cbs/mFs^
I50
Of GoMgrng;
T^ Gauge a Cask^w^khis mf futt.
X
5
6
ooo
470
830
>3
M
*J
i^
17
%
1036
]r339fi8
1420
17^41
i84^Ixx
19.8
&6
I
i^
ii7i
ix|t3i8
1405
1^30
2703
i«47
1918
30f6
3189
33xr
|33«7
34r*
35'7!
3<^47]«
37«i ?4
I3777
1390^
17
3.8
3<?
3»
3^
»3
»4
15
37
3P^o
4014
4087
4150
U*i33^
U7<?|
4338
4400
44^»
4541
458J
4<^4^
470^
47^^
481^
438f
4943
^000
5057
^74
fi34
5if4i
5^354
351^411
$47^1
3^
40
41
4*
43
44
45
51
53
55
4
57
47
4«
^o
A Table for the Gati^n^ of Wine Ca^ks
which arc fx>c full.
6: \farts.\Gs ]fms.\G0 ^fdrts.\G* \tan$.\Q. \ fms.
7^7*
7758
78if
7ppo
8071
8154
8315?
5404
8491
8$8o
Z66i
^76$
%i6%
8p62
9otfy
^170
9186
'9^9t
16c 00
I
3<f
)<35
^600
57*4
5787
5850I
^9U
?97*
^0,0
^0p4
<(if8
^*t3
6188
^353
^4(8
<?483
6679\^^
^7451
4^ <^8ii 59
<^877
69M
70 u
7d8i
7t53f
49
50
5>
7125
7*97
7^7<^
7444
,7519
I7595
6%
^l
^1
Of Gng i mi , 151
TleVfe rftkkTsUemtlm.
Fif (I mcaTinc the Diauncccis of che Cask
[atthe Head and Bong, and lb find che Con*
tent of the wbok Cask. Then aieafure how
|many Inches deep ^ Uquor is which is in
I the Cask) and then woik by the Rule of
Aropoction^
Ejumple. Ln tbeCdtl^hcm htfnt 3a In*
thti St the Mmgt snd At Uqim 24 hicbu
ditf.
As the Diameter si tin 3uHg in Inches 3a
7o the Jeftb cf the LitjMer in Jnebei 24
So the Radim of the jMt . I coco
7a the fart fr^orthmai 7 50b
Find this Number 7 500 in the Table, and
it anfwers very near to 50 Gallons three
quarters. .,
Then work ag^in thuS) omitting the final*
let Fra^ions, which are of little concernment*
GsL far*
As the CaVoHi ef the HadiOf *i 00
70 the frdpertional GJions fmni 50 75
So the Content of the whole Cm\ X07 jo
to the extent of the Liquor W^glg^ ^1
24 Jncbes deep > .
that U , formhat above 8tf GaBons and m
hatf. ,
152 - OfGakgitti,
T9 kpm tht C9tttek^,if ani Wttte 0^
Beer Cask^in Me w Beer Gattom. '
IbitwAiStiCQOpirsScsniliHgii
Fbt the Biter iatteti
iJttt TAme^ *t tbtHead i^ iiehe/ f pir-
the t)Umtur at tbe iMg 23 inebti o fiu
fbtttngltf ij Inektt ^p^i
foi the Kildetkih.
I
"fie Didtkder at the Head 1 6 Uche$ i pm
IbepMMHnnihBUttg < i%UcbU6far.
tbeLtHgib 21 Inebii If Sri
: Theft SciotHng^ do very well agree with
t)K old received Quantity of the Afe Galbn^
ivhich allows it to be 3S8 Inches j;, tnaking
ibc Bairel to be a Piat over }i Galknis;
and tlieKildakiaal^iatandlDbal^ }_
So that, \ ' ;;
iiranyntmbir of li^m Gs&oni^ to ihi Chfad
of 0^3 tf^me€d$hU Brer or Alt Gatlagu
Cut upon later Exb^lfiiBents, it hith beei
i^efolved on by the Comtnittee of ExcftTe;
rha^
that w the mcafuring of the Brewers Tuns''
and Vcflcls, the Ale Gallon (hould cootaia
but 283 Gubicii Inches.
Now for the noeafuring of thofe Tims^
whethci they be Square or Round, ot of
tvhat form foeVer they ate, you aiiift da
thus*
Firft, you mufi find the Content of fach
Tuns in folid or Cubick tnches» by the for-^
iBCf Rales of Meafiiring fuch Bodies ^ whitb
divid^ngby aSa^ the Inchei in one Gallon,
(hews the Content in Gallons > and divi-
ding the Gallons by 315 (the Gallons in otic
Barrel) (hews the Content in Barrels.
You may make this Work more (hoit
and caiic, if you provide a Tabic, which
(hall (hew yoii how to reduce the Foovmea-^
fuie of atiy Superficial Form into Barrels
and Parts 9 So meafuring the Superficial
Content of the top or bottom of any Vef-
ft\ according to the Rules of Art, yoii
AmII have the Content in Barrels and Parts
for one Inch deep, which being multiplied
by the depth of the Veflcl) or the deptlvof
the Liquor therein, (hews the Content or
Quantity of the faid Vcffel or Liquor.
There arc two foch Tables for this por^
pofe, the one for fquare Tuns, the othef
for round Veffcls, in my ?nftbdftTs P41-
ffivf> which) though (hoxt, may ea(ily be
inlargcdl
1 54 Of Qauging. m
inlargcd for fuch as have need df ehetti.
t fliati here give you another (hdrc Tables
which OiiU be more general for all F<)rms»
(hewing the dontent in Barrels and Paits
fdt any number of (Vet of Superficial M ea-
Arc one Inch deep. '
N!ii#) One Foot . fquare is near half a
Gallon i for there is 144 Inches in a Fooc^
which doubled makes :^88> which (hoold
be the Content of the Ale GilIon» though
here it is a little lefTcned to 282 Inches.
— — ■~^^- ■ ■ - •''- I . . i"-i ■-*-
>-...v. .-.• , ....- .■.;...-■. . N .'■ >-- ■ r'gr
0/ Qmiing.
•5S
F,\efmj.] \F. \B.fartS.\ |F. li.pmi.\ j F. IR tdrtsl
1 0.6141
iJ|o.4iM
I«
*-7?44
1 ■*
1.177--
I a.ei34
V^
o.4iri
J7
9.8ol«
I1
*»'9I4
i o.04i(S
J>
0.4J97
iS
o.8ii8
«s
I.IOJI
4 e.oii?7
J*
o.4ij«
5?
o.gjfi?
£6
".*i?7
I D.OffS?
iJ
0.4S80
to
o.Bjio
87
1. 1338
* O.PSI.
34
c.48it
61
0.8651
ss
1.1480
7 o.o^9i
JJ
o,4?<?4
£1
0.67S+
8,
i.ijti
8 0.1 1 Ji
36
0.JID6
«3
o.8,jj
jn
Ji'»7«J
> o,ii?7
J7
o-IM*
'=4
0.907*
?l
l.tjorf
10 0.141-3
38
<=,-J330
S5
o.piie
91
1 .3*148
II o.ii<5o
33
0.513^
5«
o.&JfiA
i'3
I,jI!)o
(( 0.170X
45
0.SS74
<;7
0.9101
?4
*.333^
13 0.1844
4"
O.J8IJ
£8
6.9*44
9t
^.J474
14 0.ijil<i
41
o.59SiS
ss
o,j786
»*
4.3«1S
IJ O.Ml«
43
o.£o93
70
0-9919
91
1.3*100 •
ifio.iifij
44
o £140
7^
1.00*9
98
i7o.'4U
41
0.1*38^
71
T.Olll
SS
i.4»4i
>8 o.i.!53
46
-M*'\
T3
•■<'3I3
loo
1.4184
t? o.tifJl
47
o.666€
74
1.0495
100 :i.8j*8|
«o.rSj7
48
o.*8o8
7i
1.0*37
39*
4.MJ^
11 o.ij7g
4?
o.e?io
7«
1.077S
400
J.*73*
»tO.JL>,
JO
o.7e3i
77
i.o9'.o
(•3
7.09»o{
'3 OJ'*!
ii
o.7»3*
78
i.ioSi
(00
'«/ri04f
14 O.J4O4
5io.737'^
J*
1. 1 104
700 f.iSii.
li o,3V4«
13 "-'S'*
80
','347 8pQliJ,547»
1.1488 9°Av;-y6j6
-<[0i3i(g«
54b.7*/o
Si
V7 0.J8J0
r J 0.7801
3*
.,.(!jo lod'9i^'.tf4C,
18 0.^^97 1
.1 .,
"f . ■
flop.
15"^ Of Gmgin^*
t
, Pfop. 131*
f # Gmgt d SUpy and caft mf how mmy iuns
her BHrJenis*
>feafure the ka|th of h^f KecUhe lu^achh
at the Mi(l-(hip Beam, and the depth of the
Hold 9 and aiultiply the(e three one by the
(>cber^ and divide the Produd thereof by
100: Sp you (hall find how matiy Tuns her
Burden ts.
. E^an^le. Ss^ofi a Sbip^^ having^ the
Ungth4ff (^ Keel 50 Fnt^ and the hmSUh at
Ae-tSJ^^ip Bjpjuf 20, iht depth im $hi iMd
|o foot I ikvo many tuns mi the Ship tatty ?
Mttlthfy ^obyio^ it mak^s loqo'^ and
ilka^ ntHftipliid by io» tn^ ioooo> ti^Hcb
iividod fy ipo, ditmg off the upo /^. fj-
ptfe^y^fyms fbe Ships hnrdtn to be lOo iutos.
^Mi this itckoniiffi is only 'for th& Kings
Burfdr Merchants ShipS) who give no al-
lowance ffn Ordnance, Mads^ Sails, Cables^
Afichor^, wbi^h are all a Burden, hnt no
TuQQag|e, }du mull.divide your Fipdu^ by
^5: >$o the forefi^id Ship will be ^una to
be ' 10 jf iTuns | f puts.
Bur fiiils way o|' rqckoi^dg the Tmrnone oC
Ships/ though it niiay come near in tcKm
^Tp^^^it imT miff mwh ifi«lMff»TiMr
OfG^HgiHg^ 157
ali Ships aTc not built of the fame fa(hion :
therefore it is the beft and ttuefi way tp caft
up cheComeDtoi the Ship inoreexaiftlyiic^
cording CO the fUiles of Art, with ftSftSt
had to dit Mold and Shape of the Ship, atid
fotoiind how many CtabtdiFeet t!hc %hip
doth con^uin') and every CuUclt p'bot of
WaiDer^acoovding tofomfe, weighs 5$ pband
4visrdppU ; But Dr« Wyhwtd imds'eirery (Dti^
bick Foot of Watcx' to iweigh 4^ p^hd^
5S8piiirs. No)V eveiy Tonbeingaal^iin*
4n^ weight, a«l tylcif)f lOo wtigi|K i^k^
popii^) ..^hfch make « 14:0 pounds ^ dl#d[e
this by 62 pound 5S8 parts / it Undoes ) ^
FocY ^ parts :> Sp chat a(Kmt }tf'>Cd[liie
F«et ip^liea Tan weight. ; , -^ 2 - > -•.
^ hcr^ta^c notice. If you th^s4MdfQi^
a Ship witbiiu yoU fluU find the Cofatem dt
Biu4ep^tbe 9kSp win hold ot take )n»^ %
yoMi QiiNllim^ the Shi]^ on dbe ovut^fide iio hec
^ighc-^muk^ at Ibc fwim ImnB u^l^diHt;
youiball hajre the wei^t>r cmtent ^of fhl
en^pcy^ Ship v and if .yod JMafure ^it^nni thU
^ Lt^t^m«rk to her full dlanght of Wam i^
; ing iadipt^ that will be the truip ^c^ips^pi
t\innaie^ the Ship. ., ., '^^.
.-.r I- - ^--■'>'
t
1-58^ OfGoHging.,
V
'J
' ffop. 132.
Knomng the hleafures of a Ship )of one Bitr^
Moid^ vfibicb (hall be iopblt^ or trebtit or m
anypoportion^ m^t vr kfsy to tbe pud Sbip^
Multqply the Mcafures of the lengthy
breadth) «nd depth of the Ship Cubially,
and tbtn>double.or tr^le the Cube^ ttml
^tia^^ ^he Cpbe Root thereof.
, I Example* The' Kid of tbe firefaid Sbip
kfhs S^ V^^^ ^nd bet Bmrdm behig lob
TPmSy to mobs motber Ship liks ^S^ efico
i i^bi.QiAe \f ^^o 1$ ^t^OQUwhicb dmbled
mskfJ 2 50000, the Lag.vfbert(f U 5^3^71940,
thjt^^d pan wberepf U 1, 7993 13. which
-Wb tke, Log^rf 6^.00 ^.phith U the* Cube rot^
ff the kngtb. of tbe ■ Ktd required^ ^'a* 6^ Foou
jlfic Jjke you nrnft do foir the breadth and
^e{^^ which f4«i iHiay th«s vrbfk (^ the
M^atithiDs with miich eafe and re^adinefk '
One &b^ too tHMJUj Log. :a^<>oopoo
7M (Ttfef/' 200 tZiiiwi 1^* ' 'al.3^'ip3 o
USal^enfite * ^.0^30/036
A third part thorecf o ) 1 003 43
Addedto one Ships Keel ^o foot i^49^fJo
OP
T
159
OF gunnery;
Prop. 133. '
'ibe Names pf the Trmipa( Members ofa
TUee of Ordnanet.
He out-fidc round about the Piece, is
cs^Ued^ the Superficies of her Metal > the
Subfiance )r Whole mafs of Metal, the Body^^h
the holtoi. fiefs on Concave Cylinder, the
B^^ Of Shnl » (b much of her Bore as con-
taineth tqe Powder and Shot, is ihtCbambeT\
Of Charged Gf Under i the Reaiainer^ her^^^
cant Cylinder > the Spindals or Ears are cal-;
led the 'trunnimi^ the Pummel at her Coy le,
thtCafacabet Veckjt the little Hole, the toucb'^^
bole ) all the Metal behind the Touch-hole,;
' here Breecb or Coyle 9 the greateft Ring at her-
Touch- hole, her tafi-ringv the next Ring
above the Touch-hole, hcjr Reiuforc'trringVL
-the nexito that, the Trtinnion-ring'^t the Ring'
next the Mouthy her tAuzxie-ring > the Ring
between the Trunnion-ring and Muzzle-ring^
her Cwnijh-ring 9 all the Rijags and Grcle|(
a[bout the Muzzle, the Frieze 9 the wholc|
length, the Cbace. . 1
— ■ » II I !!■»
Here. foUowetfa a General Table of Gutmeryy
Shewing the Lrngth and Weight itfrnoaufaalJEn;^
,U[h Or&^ce, die Diameter and Weight of che^
Bullets, tlie Leogth and Breadth of their Ladles, anf
fbe Yfoff^kt of Powder to Charge theBi> &j^ . ^
i
A Table of Gunnery.
►^•■**i
•« «■
%e Names of the
feveral Fiecgs <f
Ordnancis
tfBafe
€ Rabinee
rf Falconet
/4 Falcon *
Minion largejl
Saket /e^ijf
Sa^er ordinary
DMicxlvcx, ieaft
r
■■III ■■ !■— <i m
beibiculven <»• J.
Deniicul.(;/i)3r^
Culvtrio hafi
Culyerin ordin* '
CulverifJ. iargeft
^mi^m.yaA | li
Cannon R6y5. ; li
^^
2^
4
5
6
7
7
8
8
9
10
Id
II
ir
U
12
12
S
2*
5r
6
6
o
o
o
o
c
c
o
o
1^
60
fi
5? •*
O
O
o
o
—
200
300
400
^00
z
lOOo
1400
1500
1800
2000
2700
3000
4000
4500
48
p
c
o
GO
5490
5600
6000
§000 f8
z h
6
o
I
I
2
3
3
3
4
6
3
3
4 O
4 2
4
4
5
S
4
6
O
2
4
4
4
A-
4
5
5
^
6
6
6^
M4lHMi*i
i'
4
olr
3
2
5
7
*•"
o
2
c
2
4
e
c
1
c
3
4
Tabk of Gwmcry.
-»■*'■ if
l62 Of Gunnery.
\' ' • i iProp. ^134.
(^ the i^mni Fmifieatms »f moft fkces^
if Ordnance*
; Thtti arc three Degrees ufed in Fortifying
each Cort of Ordnance^ both Cannons aad
Culvains* Firft, fuch as are ordinarily
fertified, which are called Legitimate Fkees*
Secondly, fuch whofp Fortification isJeflen-
ed, which are called Baiflard Pieceh Third-
hii Double fortified Pieces, or Extraprdinary
ficces.
This Fortification is reckoned by the
t^ickneft of the Metal at the Touch-hole^
^t the Trunnions, and . at the MuiaJe, in
prof^ortion to the Diameter of the Bore.
The Cannons double fortified have full
one Diameter of their Bore in thicknefs of
Metal at their Touch-hok, and f i at their
Truntiions, and -^ at their Muzzle. The
leflened Cannons have at their Touch- hole
iut i<>t ft of the Diameter of their Bore in
diickoeC^ of Metal, and /<$ at their Trunni-
ons, and A at their Muzzle. The ordinary
^rtified Cannons have I at the Touch- bole,
I at ^he TrnnnioDS, and f at the Muzzle.
4^1 the . dotible fortified Culverins, and all
Ifffer Pieces of that kind, have one Diametes
jpdf ac the ToucK^hole, f| at thcTrunm•
' " «'' ' ' • " ons.
Of Qunnery.'^ 16^ f^
ons, and ^e *^ ^^^ Muzile. And the ordi-
naiy faitified Culvcjrin$ a^e, fortified ctrci'y
wav as your double forti^d Cannons -» aod
the'kflfcncd Culverins^ as the ordinaiy Can-
nons in all pointS^.
Prop. 135.
How tmch Fmder U ft for proofs and tpbai .
for adiofty for any Ticst of Ordnance.
Fc» Cannons f of the weight of their Jyon
Bulkt for proof 1 but for fervice |ialf the
weigh of the Iron Bullet is enough, cfpc-
ciaHy for. Iron Ordnance , which will not
endure fo mujch Powder as Brafs Guns by
one quarter. For C\ilvcrins, the whole
weight of .their Shot for prcof, and fot
aftion jf Fqi the Sakcr and Faulconf of thj;
weight of their Shot i and for Icflcr Pieces
the whole weight inay beefed in fervice till
they grow hot -> but then you may abate
with difcretioq. For proof pf thcfe U^tx
Pieces you may take once and f of the weight
of their Pullet. Herein alfoinuft be regard/
tp the ftrength and gopdncfs of the Powder^
which is Itjbc^dinaty Corn Powder. ^
?rpp.
*^4" OfQunmry^
To Mol^ Ladles to had ytmr 0ms witk
The Ladles are to be fo proportioned for
every Gun, that two Ladk-fal]s of Potvder
may charge the Piece , which in general
tp:m9 is thus.
The Breadth of all Ladles are to be two
J Diameters of the^ot, that foa third part
of the Compafs may be left open, fer die
Powder to fall finely out of the Ladle when
you turn it the bottom upwaids. The length
of the Ladks muft be fomwbatdi^rent, 4C«
cording aTs the Piec^ is fortified.
For double fortified Cannons » the length
cf the Ladle may be two ^Diameters and an
half pf their fhot, befides.fo much as is ne*
eeflary to fatten it to the head of the Ladle-
fiaff. Which will require one Diameter mojj^
of Plate: but this is not Kckoned te the
lenjgth of the Ladle ^ becapfe it holds no
i^owder*
' For cfrdinaty Cannons, the Ladle rnufl:
not exceed two Diameters of their Stiotio
length.
For Culverin; and Demiculverins the
L^lemay be three Diameters of their Shet»
a(nd three and an half for lefler Qans, to
load them at twice: If yo^ wiU load thetn
". « -at
V.v.
Of Qnnntty. i6^
at oncC) you mult double the length of the
Ladle.
' Obicive this for a gener^ Rule^ That 4
Ladle p Ballesin lengthy and two Balks in
breadth, will hold the juft weight of the
lion Shot in Powdei;
Bmf note, Tbatlr6n Oirdnance nmft have
but three ^natters of the Chalrge of Bnrf$.
Ordnance*
PifOp* 137.
T[q hfoit r$bat 'Bullet k fit h he ufe4
fot any Cttk*
It if coDvefiient thtt the Bullet be fcmc'»
wbe^ left than the Bor^ of %ht Ciin, that
it itr^ay have vent in the difchatge, and
not fiick ind break the Vkoc. Now fooie
think a quavter of an Ind^lefethan theBbre
will fcrve for all Gans v but this vant i$
too little for a Cannion, isitfd too ntufh for
a Falcon* It is iMte rattdnal ^nd avti^
ficial' to divide tht BDrt of the Gun kto
20 equal parts, and let the Diameter of
the Boilei be Ip of thofe parts, nccord*
ing. to which ptopqrtioa the TalHe is eaku«
kt«df
l!56' Of Gunnery.
Prop. 138.
By hpcniftg ibe weight rf one BuJlet^ i§ f^nov^
what any other Bullet mi wei^. .
tc is a common Opinion, and vcrf near Co
ihetruth, as ydu oiay fee in Or. i^&ifi's
T[aU<me$rla^ That a Bullet of caiV Imn of
four Inches Diameter weighs nine pounds
of Averdupoiz weights.
JMow if an Iron. Bullet of 4 Inches Dia-
meler weigh p L vyhat (hall an Iron Bullee
of 8 Inches Diameter weigh >
All Bullets have a Cubical proportion one
to another* Now by plain Arithmetick , the
Cube of 4 is 64^ asd ttve Cube of Bis 512*
Therefore, '
As6\yto9U 50512, fa 72/.
How to perform it by Logarithnis, you
fnay fee in the ninth Propoiitioni
fim if the Bullets be of fcveral Metals^ yoa
tnuft know the proportion which one Metal
hath to another, and fo make a fecond Ope*
ration.
Example. T[befToponioH between Lead and
iron U oinmcb a$ two fo three : Now tf y<m
wptddkyow what either of thefe Bnllets vfm^i
weigh inUad:
For^the Bullet of 4 Inches Diameter,.
<^/2) to 3 : 8091* to 13 /. %•
^ Fof
• Of Gunnery. ^ i6y
iot the Bullet of S Inches Diameter,
The proportion between Iron and Stone is
as3 to8: But this is. of hard Marble Stone
which is fit for Bullets. And in fhooting.
thife BttUeis, you need not ufe fo much'
Powder as for Iton Bullets.
By the weight you >niay alfo find the Di«
atneter of any Bullet of Lead, Iron, or^tone,
or olv any other Metal whofe piroportion is
know)i^»
The commonly receiTcd Proportions foi ^
Mctafls itye thefe.
Lisi- U to Iron ai-2 to 3.
JjeadH4oBrafia$2^toif*
LeadUtoStomat j^toi.
ikw >f to Brafiof 16 to iS.
. Iroi^ktoSi&neas 3to2. "
- The more exad Proportions between Me-^
tals ate thcfc.
Suppife^a Cube or Bullet of a certain bigitefi,
ta mi^iooi: might i thr % CuhofBuUet
of my'0phl^fe Metals or Ibingt fiall migh
at^filkmtbi and hav^ thir fropmim*
(joli "^ 'too op
Brafi ' 47 37
' hoyi ,42 JO
St^Mh^ 7 ' 4?'
Uai ' So ^i ,,
SUvtr 54 39 V^^^^ 15 80
/ Water 05 tfS ^ ^ •
i6$ OfGmmry. k
Now if ym wntld l^^ww the iigittjs (f the
* Sullet ihat ufUi vpeigb fhm nmck^ ym $Hay
fmihyAt fofmet- Rmhs^ tha m a fkdhief
hm wUfA mdgbi 9 U hath 4 Inches Di^^t^e^
ier'yfiM BulUt if Iron ibjti nuigbs 42 /; i^k
6 Itubes \ Dimtit€r% and that 4nt^ te the
magHituJe of the BuUh wieb tiifig c^ of^
th^t fivitsl Iithuli mil wiigb m -^e^t"
f4d. -
In like mraioer you maf /ind^h^ weight
of any other Solid Body, of different Mc—
ttls, fcy f hel^ Proportioof. > j j
Example. Jf a CattmH-SioyMl &f Wtsfjf
weight idooL tpei^t^ -v^M Jbalt a Gattfton
cf Irm of the fame length and tbkfyefs
tpelgb ?
^s 47. 37 for the Br^s^ Ug. Jif 755^5
2V42. 10 for the Iftni ^ 3\6i)!^z%z
Soihe^Brafs Cannmtswdght 8©oo. 3 -jfo^opo
Ih^wnyfHbftr.thfirfi ■ -jJ^TiT^
1[o th might </ th lf4)u CaUf^ju <>• ^3 18$ f^^f.
I hitye p^rc added t)ic Proporii^n^f itf^.
tct to thffe Meuk, . ^accof diqg tQ^J^;;jiiy..
b(^Td^s EkperimeiTt, who finds a Cubick Foot
of ^atef to wdgb 6^h jSSj^jm, tha^
1 find ia others but 55 L And fc^ tfa^ y^
O^y k^Qw how nouch any Pie<^ of Ordnance
^iigK^lcfsin the Wafji thiW in>thc Aif a
, For any Solid Body loTeih . fo much xJi its
weight
OfGmmry. 169
weight in the Water, as the quantity of that
Body iti Water weighs. So that Gold lofeth
in the water S I* 6% parts in every Hundred >
that is above ^ iSth.paxt: Bral^ lofeth 5 L
4% Parts IB 47 /• 37 P^^^'^ A^^ i^> *^o^<? ^^
eighth part ; Iron lofeth 5 /• 6% farts in 42 /•
id farts i that IS) above a leventh part.
Thus you may give fome gutfs bow nnany
Tuos may W^lgh a Ship being funk^ know-
11^ her weight and lading before.
Once again. If you invert thcfe Propor-
tions : Then if you have a Solid Body of any
of thefe Metals^ and \yould Riake another
ol' the fame form and fafliion, which (houl4
be of the feme weight i the Bignefs or Mag-
nitude thereof will have thcfe Proportions,
U^attr
10000
Sttne
i6^i
Tin
1458
^iw
m9
GoU
Braft
1256
Silvit
1044.
Lead
0^38
^u\fiher
07^5
o5(J8
•
ftop, 1351.
19 hfum hm fat any fieae rf Qtdnantt .
... mlljbffou
There is mu^h difference in fcveral ;^ui^^
thors i^Out this h but all agree In this, ^rft^
That the Bullet is carried from ^hc moiiijh
of the Piecf mgtc vlWently^ and for a good
Ijpace
170 OfQutmeryi
fpace in a fljraight Line or Range : and af-
tcrward as it p^rodeeds furthef/ asthc vicr.
lent force of the Motion abateth , fo the
Bullet finketh downby degrees, till it gra-
zeth upon the jrouhd. Nij>v thefe two Mo-*
tions arc conlwered apart, or elfe joined*,
together, but they are both of them fonfi-*
what the longer, according as the Piece iS
nabOnted higher from the Level to the An-
§le of 45 degrees, whiih is the oatmolt
.aridorfii arid if you raOunt any .Piece
higher, the Randoiri pf the Bullet will be
(horter and {hdrtev : So that if you could
ftoot exadly' upright, the Ballet would
fell down into the mouth of the Piece a*
gain. . ^
The jight Range of every Piecei being
difcHarged in a LieVel, or parallel to the Ho-
irizori, is fet dQwh iri the former Table, in
ivhich the Cannon exceeds-not 185 Paces-
that is, 5 Foot to each Pace : fome reckon
much more i but then they count ordinary *
Steps or Paces of 'fvs^o Foot ji and Batteri^
made with (itch Pieces are ufoilly made at
100 or 130 fuch PaoeSi at which didaace .
thcf do the beft Execution.
The utrif^oft Random, like wife of 'any Piece,
that i^, from the Platform' fothe firft gra^e
of the Bullet, I find by fome to be aboujt teh
linncs the diftaitce of the Right Range %
and
inclaccotdingly I have fo let it down in the
TaWft.'. ,■ . ■ ;,;rv .',.■ ., ■ -J- ■:;
As foi the Ranges to the other Desiees and
Foints o£ the Q^dr»Bt, I find the^ Tal^cs
in good Authors. ,1
/
171 OfQl^trjih
\ ' • ■ • '
^ . . . . 1 . _
, tbeVfe of the Tatkfif Random,
Tbis Table is ritbcr pmpdicioiial than to*
t1 ^ for it cannot be fuppqkd that aU kind cf
> Gu«5 fconid have a like^andoii) a. this Ta.
^le beft ^ffccifyg ijg Cannons and CuWerins,
and the greater fort of Ordnance. And
theireforc* to know the Random of anj^ other
iSun, yoB may firft make a Shot er iw^ at
a cemin Degree of Mountnre \ and imafu^^
ring the difiance thereof, you may by j^he
l^lule of proportion find the Random of that
Gun to iny other Degree^ and lo make a
fable thereof.
f 5 deg. fif$oU the , UuUet 41 6 'facts ) fht^
far will h (hoot hting motmed t^io deg*
4s ^22^ ibi tabMldr dij^ance f&t 5 d^g. cf
Mpuntfire^
To 416, faeoiy iht d^anct fmnd;
So the Ifabuldr £fianet for lodej^.ef JUmn^
'im^ ui4«
toikodijl^m readied. , Work by the Log.
an4 you Piall find tf^p i Pkces.
And yet it is to be &ared,^his wHrnot de*
itevfnioe the bufinefi fo exaoly as it fhould i
an^ thet^dfoKe it wete a very good Work fat
romei who have sl^Il tnd oppoiitunity, fo
piaK < Tri ri b y feveciU4^kces, andtojind the
' * Ran*
Kandom^ of them i aod^inake tmitr^ktOt
Tobies for all wc commbn foyt ofn^iglMp
I ^Qd. itbat ^Asijiye in his Oaniiefy^ itiadb
fome &YK<^i«rient9 li)^ ;ii > Bike* m wb fHflf*
pofe. The Sakei was 8 Foot long, ^i^
he loa^ wttb fhtce poudd^ of ttoWdUti'^x-
adly we%liing JtheiPow^ andrthiiiw^'^^
vcarytlioe, raoxfitjiB >k dowa witH foifih^^
^Dtl (jtrohes as n^rasfae could v$Ai^ tUrij^ifUc
put iiQ Wftd upon thip fittHetJ^caafe yI« tftras
W^. qWURted i * afid thuf tie made foui ^hMf,
eacboi tjbeaihatf anhomaltei^ttliejdibeiothtfc
the Pieoe nii^,xqpl,:aiid''bb ^ffedudbtdM-
^%i aa4 ffioUoted hts'^ksfif to'fout fevetdl
De^TgcfkCi|.Nfountulra^«iid.ffiJeigi j^iO'^Jf itg.
loifef and found tbcfe Randoms vy> s^jCJ ui
I, . .iai$ - \ \ ^ 7^ V 5^'
* 3^3 i i 9 ^^
J 4ltf
< > 1
:/
Captaio
f
I
?74 Of (hmierfj
•j : Oj^ft Bsxml ia- his 'Bobk o( Gvmif^ry
t.ft^^s^ hitw by ^ tindiflgtout «he Random of a
Cannon for the tiift Degree of MoUfitaifevto
Jtoijt^ Staiidona for evcp^. Degtee to 4^ ieg.
. vfaicb^ the utitaefA Amdem, afreif tliis fmn*
roFji^^^ oat, h0w; many Piecs tJieC^n*
^tstwillrifciboi hK»^\ilAiA&K^ by the Metal
C^WlAob tfcascotimslfoc ooe Ddgreeof Mdai>-
:tAk^i4ra(le tUub diftaboe^by 50, 'and> thdi)
:l»iii%^yjhe:Q2>ticatfby 1 1,. «^^^*«^' wiV
,kirig outthfi^mmber.of: drt^tdat^ d^r^dr-
3Qr)!c:v^ifibidii^:WtW(edn Rang^ ^^t^g^^
»fl^bidirjbaidg divided , Iqr 44^ . < tfce -Q^^tk hi
Ifteiidi fhclnynihci^faPadbs ivhicA tliis^ Bui*
J<t jrUllbf^ v^^^ .§tbex Ranges from Degree
to Degree; ?.TinlrT- a .. .•-) i^- -''-''i f^^'^*^ S^» -^^■
ih' ^c UiXd.. 1^1 j^h^ his ^Uh i^H HeJ
\ooo oriSmafy. ^aqiT^4fmt^t-ifld'^aU.^hSfy9
^ijOmt^Mll gmAb^i^mbkb behim^lh
td byii-i it mO give 2ao Pacesf Whkh^U^ iht
nun^rf the' text digreffion M^in'tbt^fe-
cmil ^grnV<j9fhich 22C| divided^ by £^y the
nunihi^ of tbt remfining Vegkt^ yields 5*
vpbm ^ *be mumher of faces $0 bt dimikijhed
in ^acb follomng pegrfe* 4<^(( accoSding
to tik\s^u\c (bis Tsible is;franred< f
• ' . . . • 1 i <'^^' I
... /;) s M A
OfGrntitay.
>75
A tAIc of RanilOTiA lo 45 Dc^rrtsi'' aC-
coumiDg 3 Foot i to the Pace. "*
P««
dif.
p««
dif.
077s
22s
23
468;;
,n6
I
1000
220
'4
.479t
■OS
'. X
1220
215
25
4900
100
..3-
■435
zia
2(
yooo
95
4-
1»4S
i°S.
27
5095
90
1-
1S50
200
28
5185:
■l
A_
2CJ0
»«
-«
52^0
1 1
2245
i^4JS:
190
■8ji
-'
. !9l5S5<>
- Lu Ji2S.
« S5«a
: *34 5620
^.^
^i6
J'tf20i
lia.
■
. <5
jSoo
■75'
,.
6g
»975
■7q
,
• SS
|tz.
JI4S
165
' Ss's
5«75
SO
an3
»3io
169
w;**
57M
45
•5470
'SS
577°
M
3<S25
IJS
gj8
5810
SS
J77S
HS
59
5845
30
'I
3920
r4<:|
40
5875
^5
; ■'.
40(5cjii3j
4^
S900
'^20
Iff
459 s' Fjo
42
JS>20
"«
zo
43 »S 'i?
43
5935
10
-.-ZI.
445° 'io-
- 44
J94S-
'"■"'.
22
4?7° "}
4!
5950,
Mj
r^«v 0/ Onmieif.
But this Tible of Almmiir !iw>a, ii»
all forts of Otdnance, I jucoqiu one of lh»
-s— J t-_i_
- OS-ti ^ M + O "^ CO
«4 O' * OQ-H «JW O «
foJwi ^'^ <-«» O I" «
o; 5 o o Q o &
i
B-S"
:s>.
0/
CfGmnter/^ %j^
•
t
Of Shotting in Mtrtsr-fitatt*
AS Cannons and other Pieces of Ord^
nance are ufcd for the mofi part to
fiioot forward near a Level » fo Mof tar^piecet
are uicd^forthemofi part to flioot upward^
and at Random : and therefore the Ran«
d6m of rhefe Pieces is rery neccfary to bd
known. And moft of the Tables that I
find hereof agree in their Randoms, though
they are in a fever^l drcfs> fo that on^
wei)ld think this were fully and certainly
known-
Mr. Ntfifan and Capt^ UtMm make iii(b
of Vu^o VfanQ% Tables, the one for A;
I? Poqns of the Quadrant ^ th^ othipr foe
treiy Degree, takifig the one half of each
Nnofiber, and fb r^ndng jj^into FMci of
f Foot.
M4 ri
W.8
OfGitamrj.'^
- ■ - - - - . ««
\ Table of Randoms for Moitar-picces,
.«9,c|rciy.P(!gi£coftlKqaad«llt.>
;
. .100
.891
23
480
. 66
, I
122
88
24
4S0
65
. 2
I«
«7
iS
500
64
■. ,. «■
I<S4
86
26
JIO
. «3
-4
■185
8s;
.27
i't
62
J
204
84
2«
$'S
61
6
.224
1^4!
3 262
Ji
i^'
.531
60
i '
$82
i3o
J'"
SI4°
ii»
1.8
sSi
531
is8
1 °
•S,o
MlSo
|8o
.
1'^
«H3
Js7
^297
V?
v''
^!49
J"'
SH7
= 78
.'34
a<j6
C;5S2| 'HI
3i6
a, J,
■^362
.7!
R37
is6
S«l*"7
3-7*
^38
§57
"lO
V392
7!
39
"577
,SC
'7
406
72.
40
580
4P
i8
419
71
41
S8i
4t
19
+52
70
■42
S8.
4
20
44?
<i9
43^
583
4C
|2I
4S7
68,
44
584
' ZZ\ 465I «7
45
S8j
Pm£0
Of Onnnery. ?79
Diego VffoHQS Tabic of Randoms for Mox»
lar-pieces, to the 12 Points of the
^ GuOBCfs Quadrant* '
583 570 534 4^8 377 H8 100
tf 5 4 3 a I P
fi 7 '8 j^ JO II 19
583 57Q 534 4<f8 377 24* 9
Here> according to Mr. Uartons and Cap*
taiOvHeAvmf'f Bra& Figures Ikrcoft f to re-
prefent this the moit lively) I fuppofe the
mortar to be placed at h the fi:vcral Rao*
doms are: the Pricks in the, middle Line;
Qumbred with the Poikits of the Quadrant*
forward and backward, uato which the (e«
veral Randoms are fet. The fir(\ Prick ne^r
to O (hews how far the Bullet or Granado
i^ (hot from, the Mortar, being leYelled Point
Blanks and this is 100 Paqcs. The fecond
Prick is the . Random when the Mortar is
roouhted one Point, that is 2 48 Paces h an4
fp the Randonos increafe to the fi^th Point,
which is the utmoii Random^ and is 5^3
Paces.
If the Mortar be mounted higher, to the
7> 8) jp, &ۥ Points, the Randoms decreafe
again^ as before th^y did ificr(afe>. which
they
they fuppofe to beitifach Proportion, th«f
<he Random of the feventh Point is equal
jto the Random 'of the fifth, and the Rn-
doo) of the eighth to chr fourth , and of
the ninth to. the tMrd* and fo for the reft of
the Points, as4n the 'Tiibie^ .
But here is a gi^at miftake m the^ latlet
jK^^ndoms ) fqr * if you ptoceed thus, and
make (he Rtindbfcns ^qual to ea^ othfcr, ac«
^ iDording as^ they . ue, i^ftanc (torn the/ Cinfy
Point, which is the utmoft Randocti, then
theRaifidomof theienth Point'wiHbee^fial
to the Randodiif the fdcond Pohfit, and the
l^andom of the elenfntk to the Randooi of
. the UfA Point » and fo the Random of the
twelfth Point will be equal to the Random of
the p Poirit, or the Le^el Random, vrhidi
is ICO Paces from the Moitar, which is con^
frary^to all Art and Reafen. For if the Mor*
fat be mounted to the Itwclfth Point, that is,
bolt upright, the BuHet: or Qtanado muft ^
f itionally (all down agaiit either "upon or neat
qntioihe Mortir, and not too Paces oiT, ^9
jthey mak^ it by this fuppolition.
And though they have (as I fuppofe) feen
the err^r herepf, yet they^ have made a very
poor amends for it, by making the Random
pf the eleventh Point 24.3 Paces, and the
Random of the twelfth 00% making tb6
^ifferenqe ^ this. Random asnuM^ as twoof
' ^ fh«
/
1^'
Of Qmmfry. xBt
^e other, and To drowning the i cp Paces of
dieLcvelR»ndloa)» as if they wcte nothing
coofidevabkt
' The like cnor U in the Table of Randoms
foreveiy Dqgfee> whidh noake the Randongr
of theS^^b^n to be 100 Pace$> and yetfets
thofe reverfed Degte^ssa Line forwarder than
they iko\M be \ ' for poihould be againfl p,
and fo the R4ndpm of fo dtg. wil) be lom
Pacesirom the Mortar> which Ihoiild be in
or near the Mortar, as beforc-iaid^
And this error is fo much the wot le, bei-
caufe the Mortars are pooft i^ed in the Ran*
doms ,aboire 4$, where the chief error Mes« ^
it were to be wiOied therefore that tiiif
were rciAiiied by ^Xf)erieiice and TwX made
of fc veral Monaisii AH that I can do at pre^
fent, is to give you Mr. N^toif's Esqperi:?
ment by a Uttle Mortar that (hot a Bulkt oJF
j^ Inches DiaflKter^i the Chaonber whereof at
, |thc Mouth was two Inches and anhajf Hv^
Ipieteir, «aiid ^hrce Inches deep % the Chacc
ipli^s deep, which be faded with Ihrce
ounces of Powder^ and difchfurgingitpt fer
yeral Moi^iturcs aboye 45^£|;« found thefe
Randoms.
2%e
2 Of Qunmrjf
* • * -
\
45 750 . t.
<5o jjyto ' '
4'5
?5
*^75 v3tfo \^
So 270
8 55 -|'^75
13^5 ^575
?P
« I , r ■
I
.. Thcfc Differences are very. unequal) which
ather (hews there is fome fault id the wri*
ting or Printing of them, or ^fe that it is a
difficult thing to diarge a Piece e^ally,' and
to moutit to a certain Degree exadljr i and
cither of tbefe may caufe as mudi difference
as is in moft of theCe. But yet I fuppofe the
Experiment in general is more confonant to
truth than the former Tables and there-
fore hereupon I (hall frame another Table
0f Randoms, which I hope Wtll be of*
gjbod^ufe, and not liable to the forn:ier Ab-
(iixdity.
OfGrntiity:
■iSj
A Tabelc of Randoms io» Mortar- pieces, ac-
cordipg tbMr. Mirta^'s Obfervilion,
reckoned iri ¥atds.
D. rtrdi. dig.
7 SO
4^1. ■ 7+<
B. XtiA, i£f.
Iv
68
6,
70
■ 7"
7*
- 7J
I 'J
|76
78
•79
506
+510
■ 4741
4S7
45»
,4»i
.40i
J 182
1j"
K!4'
J|339
r,298
^275
■^251
>3227
^202
W*
'4*
121
,9!>2
062
oji
000
According
OfGimHeirj.
tiling to this Tabkl haVe drawn a
Geptnetrical Demonlivation of (hoTe Ran*
^ whcicby the& things may ^ .made
plain and vifible> which though it
much from other Mens Scbemeithen;-
I doubt not but you will iind it much
^he truth, efpecially for the Ranges
above 45, which are chiefly peceflary. ;
AHb having made fome Experiment^ here^^*
of, I rind that the Randpms of other Ord-»>
nance are very Irregular ifiA defedive, eipe*
dally in iheir Rat^oms ; abover 45 i^g* but
ihere being little ^fe of thofe Randprns^ I
fiialllet it alone at* prefect 9 till foniclarthet
Obfervat|ons arcmade thfereof.
This error proceeds from the famequifeas
the other, m. they do not reckon or pro-
portion the iiift or Level Rang< anK)Qg thcie
kandoms above 45 v anc^ thi$ makes moft
think that the* utnpoft R^ndpn if apt at 4 5
4cg* but fome make it at 4a or 4} ie^. ana
fome at 24 : but it is certain, that the utmoft
Random muft b( at \^deg. and if AieRiui-
ges above 45 are itruly |)roportieMed^ they
will be much different frdm the Dtgrcjes un-
der45, efpecially towaijds the 90 Degree,
as you fee I have found: it fpt tjv: M^tar-*
piece. .
N
Of Gtmnerj. %t$
Tbt %>fi of tbh Table mil be E^Uwed
> bj thefi two Prop^ti$ns. i '
Prop. 140. *
&fiffofe upon trial y<m find that yatr Mortar^.
fiicty being mounted to 6^ dig. did find belt
Granada 700 Tards^ and you difire to jiftom
botp far it wiB find it at 45 Degrees of
Hnmture^ tvbicb if thi greafeft Kanoonu
Locke in (he Table vou fiiall fiad agatnft
6 5 degt 5 50 yatdi^ aha agiiofl 45^ dfg. 7 50
yards I • Work thus 4)y < thefe Niiii4)|u^) ac«
cording to the Rule of Propoitiom .
,^i550, to 750; 5a700,#op54i;
'Thatis, V -
i</550) #0750: {ibe tabuUr Jiflanqisfdr
^fiid Vegrees:)' •
S& 700 the Vifianee f4mdi^ Jo ^54! ibe
Vifldnco reqmted.
1 • • 1 / • > ,
i ^ Prop. i4i#
fhdiHg'ilhii a Mortar-fkce^ being maknted
69 degrees ^ fends a Granado^ 600 Tatdsf
Wbat Vigret rf Mttnttt&e nnfi that tdoftdr
have to find tbt Granado poo Tards f
>Locik in the Table, and againft 6f deg^
yoa (hall tind 4^0 yapds > thi^cu{>on you
may
uj yjunmery.
f work thus by the Rule of troportion^
As <6o, ta 4^0: So 900^ {9 fii*'
Look this Nambei in the Tablci^ or the
reft you can hnd to it, which is 73 7, and
i flaads againlt 47 deg. which (hews that
Mqrtar muA Be mounted about 47 ^e^.
47 »^g- 79 ^^^^ ^^ it may ferid th« Gj^anadb
yards, according to your ^^ifire.
[ have here omitted the D^roes under
, becaufel fuppofethem.urelers^ for.thefe
)rtar-pieces arc not ufed for Battery, as
nnons^ to (boot agSiioS a Wall, bviC to
ry Gi;aoadoc$ wi Fire-balls Qver a Wall):
)W 4^$ dig* of Monmura betn^ tHieiir ut-
)i kandotn, if yoa would have tiitto tp
ry (hortes, it is noore convenient to.loounc
;m higher than 45 deg. rather .than lower >
';dfo ihcy will not l£) their ifitcnfJcd Ek-
ition, and fall fo perpcndijPL^^rlsf upon
Hoiifc ot Tfiyifa^\ Put . if y w hajfc aay
cauon, or defire to know tjie , j^;(n<}onEis
der4f ^g. you may make u(eof the tor*
:r Table of Vffmosi which I fuppofe is
ich nearer the trucfi for the p€|^r^S'i}n<ier
, /than ^r the >iegr.ec^ *^Vfi.45^h as I
ircacrapnOr^t^d^jfOu WP,\ ^ ,\,
#
.1
z'
/"
i
'\
t . •
'I
1^7
» • -
■*M^*>— — — *i^^i II ' li — f^i^ III t^t^t^mmmm turn
I p»ii ii I -II I I J i li 'i M i* . f i I " ■ ■ . !■ J II I J ill I P
' 1
«- r
DIALLIM
«• & . % '
A'
PfWt 142. Dial 1/
N Equinodia[ Fhne h that wl^ich Ii€$
L parallel ^ the Kqujnofii^I, and is an
Horizontal Plane under the P0I6 Tijisis the
fitfk and pUin^ kind of aH Dials^apd 1$ inade
by drawing a Circle ts brgf as the plane win
well allow V *_nA dividing (it into a4.e^u4l
wrts or, Hou«, whicbyau may fi^Wivide into
Halfs and Qujurtcfa) aria fet up a Stik or Wyrc
dircdly upright mthi:; Center. EvctyHouc
is X 5^^ the iialf H^ur 742^£. 30 miiu
' ^ This Dial may be. made to fetfbanyLar
t^ud|ei and of ^Qodiiie to Searqep« {
-, ^ * ■ ■ • ',' '• ;
Prop. 143. Dial 2.
A Polar Pltt)C is* one that Hips parallel to
the Vck^ and is an pic^izonta) Pial ^n^cc
the lp^Hino<|i»U > ::'.
iW Of DiaBiHg.
(d ian Lii i fe c rofs thu nftidfl of the Plant , an d
crofs it at Righl Angks^ith theLincofEaft
and Weft, Then acAroing to the bieadth of
th^ -PJanc. vfiu jnay jpropQjtion you Stile,
whofc H|jpft Auft 14 equal t^' f he |jc^(i^'
_ JBf ; but^od raly fitid-it^migKt a^forbyStfY
other Hour-lin^. according to the Hours you
would have it con rain,' •fcftiiis Rule.
]kfthi 'rMH ^ ■ ^' r h '■■'''" ^ '-■•"* »
1. I
f
ft ■* • « 1 ♦
- ^tfemviiiiiMfift -Bt-ajt (itkw« pktaj'- '
NeeSIe 'R^idt|ghtf''6^r4 WVt^ *^ac A> lie
parallel tb^m ^M^'kmmtW^ c*Mt,
according to the Height aforefaid.
2« i»«i^ff a Vial Hpon a^ertdioH tlattet rtblt\
^the Meridian, an^iiath tW^'ra^ei^,PolIe't«-
qfjmaSwgi) 189
mtii^-Ss&y^th^TBfthbt toward ibe^eft.
' -T^^make Dialed this Plane) IRrft ftoththe
l^mtCoind on the Ndithiide of the Platiev
aocbcdin^ip^d the Latitude hi the Place jraw a >
Line wtli(i6 may lie parallel to the E^uinodi-
al i (l^tipt^wavds the Dppei Side of t hei^ane,
on (hciJSoUth (ide, draw another Dneerofs the>'
foroveant Right Angk$» which m^y point di^j
tcStW^tk the Pole of jthe* World. This Line
RiutrQandYox the Hour of :VI, and iouiA be
the F^ace of your Stile or Subfile > and having,
found a convenient liength?fer the Height of
your Stilft^. as in {he fbre^ing . Propolition;
tftc Qiftapce of the ;Hour*\ines will be fouoit
anfwerable thereunto, and tmx& be. dfaWn
parallel to:the Hour o£ VI^ as before they
were loj^eHout of:XH^ ^::
Sp ib^:iastJBPjftqf any HoMs^D^ancefirtfrn^ixi
To ibeV^^hfteif fwmAe S^fiUu " : '^
• *•; ^1 lo- .-^ ■ i • " I-j:.! / ".'.■' i
■ v--'ij:'. I Prop* f 4.^r -Biak :5* •• •;"» 1 /v -v
This is one of the moft comnnon and beft
fort of Dials, e(pecially in our oblique He-
mifphere, which being well placed in an open
]piace, (hews all the Hours of the Day from
Sun-rxGng to Sun-fet.
N z - To
190
Tonmltc it, faSi i}rs\)f a t^iw icfofi >fi^
middle of the Plane ibr the Metidiaiiori^iour
of Xllv then ^xofs thi&Linea Utdei)«|0i9^'
the Center with the Line of E^. and W« wh«d|
]s to be tt^e Houi o£ VI* The intei^bftieiiQiF
t\ii:ic two hmes you miifi x^ckon for the Cen«-
ter of. yoiir Dialy and chct eon d«fisrifaean oi>
fsak Citclc for the dramiog yoini Hoiir-iines
ii]f, which yoil noaftproporttioq ac(xi|£(||^
the Latitude ci the Plaoey by^ this RuIib,
^ ibe toffgmt ^ tb^ H^ frm tfifoih
^0 tbt Tsn^tnt if tin fimr-ihte frm Ai
TheScUeriNaftbe' fixed joft ever the Meri*
dian-line, and make an Angle froi£Piihef lane,
fbqual to the Height of the Po|e« • ThaHouts
before VI in the Mnrning, avid after Vt In
fhe Evening, maybe fiippltedbytlieif oppo->
fite Hours on^he other fide the Gehfef •
Becauffi thefe kind of Dials are of to great
ule, Ihavet^kcnftnsl^IeeptbF l^ngwun-
ianui wl^erein the )Hou|-Uiici ave calculated
for many LatitudjCf.
• 4
v.
r.
'i
» U t 3 3 *
S 9 to n n
t,
tfttK/aem fye ipo ; t^i
V
« <••.
/ '
— t I
'V'A Tabic llk«iai«ibI>lMn<:e6fdie
9k '
1*
Hour-lm« from the Meridian in
th« iepcci of Laiafc.
s^v
p
■ TUHimifrmtUMttmu. .
P-ft- *i, i;x, Uxi. iiiinii-iTiTU. flvi,
$■5
aim MJD. if{D M{V U[D MiD if
■ ?
5*
7 J»
«« * 14 }4 ,0 I4j^< 49
90 rid
3»
» !»
l« 34 " "4 1> 4' 't ■«
»op )?
J'.
8 4
7 i 17 i i 4* )0 6J 6
90 JB
J]
8 17
i *7 »8 J4 4} '7 «J 4(
?'0 57
u.
.',■,'-'!
,> „ .5 I,ji, !
«t4.
gtf ° 5*
J(
*4
lH »o -9 4? 44 46
«4 I«
17
J«S'
« i<
tS 41 JO *T
41 i«
<J 17
J)6fr
J4
J?-
» >
19 S fi >
4» 9
-S S»
$0
53
»8
1 IJ
tf J4 )« il
k^l<
BS 19
i*^-^
(1
a»:»p-?3j
»? r 11 9
1^ If
<«,!!
»o
li'
:*0
9 ^6 la »1j» 4v
41, .1
*7^lH-9^0
It
4'
>!S
10 43 33 '4
4! 37
*7 41 90 ,Q
'^
**
" 1 n 41
49 13
<J^ 1 > ^0
4J
■ i>
ki 19 34 li
« 44
it Ji9i 0-
47
44
ldUt4
1* 5oIh 4<
!o 14
n jl^ e
^
^
Il4!".>f!!-H
<o 4^te» 14 90
«
46
'O I4*» J3|3* 44
Jl ifi 69 JJflW-.*
44
47
:;,5
",53 i« 10
SI 43 6t 5390 ff
4J
48
13 li ge }I
Jl 9rO ■"90
4»
49
11 «
M !' 17 1
Jl ij 70 ifly>
JtL
19
.. i«
'3 I'
37 ■;!)! 1 7« 4) 90I'
40
ii
a 4^
'4 9
37 !0
53 14 70 )a 90-6
li
l»
ir i»
11 1«
3» "5
Jj 4rf 71 11 90
U
.* *^
H 44
S< 5«
(4 » 71 17 90 C
17
u
Ik 14
tl 1
3» 19
<4 5* 71 41 W-9
}«
yr-
n-.j
H 11
if l»
14 JO 71 J3 »o <^
!!
;w
•» ).
« »
» S'
ff ?(' 4>o«
SJ 18 71 16 90 c
14
',5
"■*
li 49
',0 nr
3*
t. 4-«'
i« !
U 4* 71 ^7 90 «
!'
'iLt*
.« IJ
4° 3<
jtf 1 71 ;S 9« c
M
4" V
■ a
ia-
Pa
192 L:: » C^: DidllwgA
-1 1 1 <- • 4
TV iwtf^e i'B»^<?ff _S^^ Mil/. . ;
^ -Thii Dhl triiift (land uprlgbfi ^hsw*i^ iti
. The Making^thereof tis in a manner; c^^am<
with the Horiionftal. The Metidian^inKj mal
i be dxa^n perpcndioilat ]iift in ttie tnidft ^f rh|
\ ^lane v the^Cenrcr! of the P>4 near the to^
! theiicd^ the Hcfefit of the St41e inujft be aii
^ An^e equal totbe'Cotpplefnentic^ thePoleli
i mid thi^ Hpur-lines rifwd be du>«;ii| a(^(|fdiRg
j to ijts Height aboVeiA^e Pllnp, which you may
; ^iihtttftk^outjdfthefounetTaMfe/diCakw.
! lat^thenfbytheRuleof thelaftPropofitienj
I As\iU%adiiu, <:-'[ :' r ^' : -
$9 fbe^^ngeut of the Hoi^ ffvm ^i-^in^ '^ \
XrihgZ'fmgmi. if tbi ^Um-Vm ftm : tU
f
Ptop. i47# ^0ial7^^«
1- 1-^ ^f^ mi^t OH nftigUVtclining Vid.
'. JTft^e fcialfe are td be;f(^t on the ijcfi ^f in
|l<>ui^,V which cliougt) they, may be Spiither^,
f e| moft times they decline either toth^Etft
orl Weft, miore or fefs* • • f - r | f I
. In theie Dials the>fertdian-lifie ha^vi^y^ a
PcjftJCftdiciHit, dfawti either in tbc^ttiidfttof
f hfe HaniX9« r«hf i<<fl7f^t
- • « "^i*
whde the Subltile and |ipur-Jirag #.9>cft.
Firft, The Angle or biftance of tfie Sab'
To <iw 2angtMt of the SMhfiiUj Vytdncf from the
t ^^;^W I^igTu of th^Stijeib9fe t^? Sub-
ftile. Thui,;- ./ji .f\ M\i '>, >*"•.•;'»•' ■ux^7.
3. The Difference bctweca. the h^etjdiart
'ortfic%fjev and the Mcridfafi-of CfceRjirt.
^As we Shie of {be LatitHdey^ TCo tiA ^Latttuii
_. ,^ ^^. LatfL.^^^ *. ^.- — "2,
^"th^a^f^enrofihe VtiUfUmn, to iheltaU'
\l^t of. sbl Differ ence of the Mefi^^^
- 4.vnrb& .Ao'glc^ 6f the HoWf-^h<» fr6ilt
the Subftile-line, which is the Meiidianof
the Plane* ThuS^
R4 4
*94 Of lih^ing.
Ai ibtpiSfm^ to the Skfoftbe Ht^J^tf
ibe^StHtist^dve Plane:
169 fb^'*ttingeH$ of the, ffotif^inefnm^tMk'-
rUiatriiftbe fbnti T!^ thttMngm of iht
, ffoHf; line frm tbe SnhfUle* , . .
For Example hcrcoFiiL^t us foppdfe the
Diit Fii.7. decltrting 45 Ag. to the Eaft-
ward in th$ Lautude 01 Loifife;! ) which is
about ^1' ^^. z o min. Were to be made.
•4 V «\
I •< V *
I. AstbtKadm 10,000000
to tie Catang.if tbi Utirl ^^qq^*
^- oHoftbeFiHe^i.' i fz!t^
TV. ^:taHeffit (fzpd^zim. ^^ $Qcpo
whUb iiii>t ^jpijiamaf the. SiAftih /rem iht
hterididH^
2/4st%elk.adm ' \ 1 0^00009
!?a #5^ dofine of the tkcUna-^ ^Q.^\,ib^
... ^ t^^^ofine oftbe Latitiulc\ ,
51.30 f 757r^>fy
» k l|l ll * <l»i
to ibt Sine rf 26 d. ym. ;^p)tf43^34
i^pff i^tkt Hci^ . if the S^ih Hbm tbcStA-
f
I ^ ^ i'^
So the tangiHi of '** l^'^^-J joxooooo
to fh tangekt vf ^t d. $yM* ia,id^5if
irUtfi^ » ^i&^ pj^rfHce of iamMMHf. r mt it
fh Viferanit if thne iH^bkb k bHwim itlt
H(mr4ini of 12^ wbkb k ibo Mervi^ of
th P/^e,. i$n4 tht Sulfiite4inej^ vphkb U tbo
Mtriifian df tht flant of JSaU
Kowlaflly, To find chcDiflance of the
ffour^Cnes from th6 Subftiict which is rhe
McridHinof the Ptane* we havefbuttdlhM
the Meridian of the Plane diifers fironffie
Metidian of the Place ^tdeg.^y mlM* it-
ccrditsg to which yott muft make la Ttbte
for the DiQance of the other Hour* lines, by
adding or fubtra6i:ing 15 deg* for every
Hour before and after 12 out of this Dijfe^
rence of Meridians^ trhidi here isrfriBkg*
57 mm* until yott come ^tt> the Sabfitle, and
then you muft add the Complement df 1 $
dig. on the other fide the Subftile^ for the
Hour next following, and 1 5 dig. for every
Hc^r after ; So you fliall bive me Diftance
of all the Hoars from tdie Sobftile > and tSiea
/ according
according to thefe equal Angles of the (lours^
^p^^aCfin'3uh&i(cVeTil ^Arclid wbcH^i^^
Dfc cofrefpon^ent tlmethito i]pOln(t];kc F^neby
l^c^ufd^ ^:diqtr4\ AehicH.iacbinm^ iH all
As'ihe^'K.aSiilfi .\ j;;. v..j',i.'.v
All thcfe tI\isiajy9pjnay.coMi9^qs?. Ta-
ble after this manaer. ' _
''mPmfrm^^nmm^u :.v p: h;. .57
^ l\i:: .li .'...jj" 'jilJt)) acn-'. jjv'/l'jrru .j\L;. "^
\f ..'. i ^ •: ■ ?i i vu . . i-. •' ! r , Tbc
* ' 'X ^ «
i-*.' « * !. -'"ill il«fill.« "^ V ,*
I ' • • V .' «■ ■ r ♦ - *
• X
*u »
«g7
«■ 4. I I V
« . 1 >
The Eall DecHner.
■<»r JL
i*» ■ I
wi
v'
The Weft DcdwffM
^——— ,!■'■■ » I I II I I , ,^ I
1'^
I
5'o
6
7 ^
8 6
9
JO o
II o
X2
lb
2'0
3
■ > T
8
3<?57
5V57
66 :sy
3 '34
^«»- Sub-
ftilt. ftiU.
6 57 2 1^6
^- to 3
29 21
81 •5^172*17'
V - * • ■< YJ • • V- •- « 4 ^ J J if
CI '6
k ^
'.<
r
: 2r
f9f. ^» fft*
Ht:o 8f 57 7'i^ if
?i-6
.<
66-57
3<5 JTI
JO 6 57V
Skb- Sub-
■jiiti. fine.
V 4« 8 3
'5 0,23 '3
6 O'iS • i(is>'Of
29 2P
ir 5J^Vp'!-3'
7 o
8
68 3
^ olSj >
4 »■* ^
3 34
+7'-3'<
Hcr&yputnaytak^nbticey Thai fifayingfBy
thcfe liules found the bittances'of the Hour-
Itnesfbran Eafi^ Dedinet, you tmVliy^eofi-
verting the Houis fitrii' the^ fitid t)ift^tT|bt:9
for a Weft DecUner >' as ybu tnay fee by cp'tfa-
; ^ • paring
19* Qfl^iMBiHg.
pm% this Tabk and che Dial, Number I*
I ogedier.
But note here, Thoosh I ht?e fettkmil
ctic Hour of ) iti tbf li^mtng for the £a4
Decllnert and the tlc^ur oif 9 in the Eveoio^
for the Weft Decfiner ^ y<t thefc Littes mul
not be drawn upon the Dials $ for the Son ii
not rhea above the Horitotr \tk that Laltitude*
and the Lines will fiiU ad>0ve (he Horiifoiical-
Jine of the Plane^ eichet of which aia)r ferve
to dired you what Hours to fet ujpou your
j;>ial: but yet they are tf ufe to driw the
.copofitjt Hours of 5 in the afternoon in the
^aA. Oeclincr, and ip io the morning in tho
.Weft Decliner^ whi^ at fome times: of the
ilTear will be ufeful ikpon the faid Dials.
;\^ Laftiof all. If the t'ace of your Dial be
iq the Northward, yot| muA turn the Di^^s
, the bottoms upward, a^d reckoh the Hovits
. the coiltrary way^ io the South EaftDeclr-
Bcr will be a Korth Eaft Decliner, and the
Soutli Weft l!)ecUner will be a North Weft
, Decliner, leat'mg out the Hour-lines (whieh
will be needleis) before the Sumfetting, and
after the Sm^rifing*
There are many other forts of Incfifting,'
. Dcclsiiifi^, and Kedining. Dials, which I
omit,' t>eing notfo craamoh andneceiTary as
th/tit: Alio for the drawing the Alimuths,
JO^ioBtefSy Signs of the ZMi^ck) Onequal
Hours,
Of 1^09iHg^^ I^
Hotirsf fndthc Hochts ffon Sm^tifii ^ G^^
for ^hero yc^ muA ^pnfuit larger Treatlfesg
wbkh ate very iveti explained and applied,
with &veral Scfieitib and Fij^ures fdr the un»
der(la»d^ng thereof, by Mr«6i^«rer, hAt.ffelb^
Mn f^tr and n;>any otherSf
As for Iqiftrunientai Dials, as Q^drants^
Rings, Cylindas, which depend upon the
SunsHeight, I hiVe added the two following
Tables pf Mr. Cunttrs^ whereby his Qua:.*
drant aqd all fucb Inftruments may be i^e
fpr the finding of the Hour and Amiutli
ip the latitude of l$ni0$ \ whereby al£> you .
may take the Declination of any Wall of
Planeg^ smd fo m$die a Dial upon itt r
^'* X ! ■ " ' ■ ■ -J ■ ■■ ' . I I ■— |W -H I I II ■ %'
A.
1
' *-*♦*!:
tsJw
— . 1 *m 1 ^ -r-
.®(\i)i.:S6'4j*CN^ <^^
v.»
) I
o o COM >cy p t^ o
^ I-' t«> VA» VA> 04
O >0 00 0^ »j ov 00
1^ CM V» VK>
O *** wt v>i jfc.
ON^ 00 ►H O M
A
'*^ *^ ^ I hH
»H 00U« -Vl Q© >J
^-^ t^ 00 Ov 00
"1^ 1»
^-^ O K> O
~
Dijiance from tbt Souths \ g^
ooooo. 0000000 \
r
>
•
>
?r
0.
s-
rt .
a <
(A
B
3-
5*
S'
00
1
CA
(^*
>
g
r
0\-|^ N 004^ y:, ^ VI >0 •-• ^*
-i^-f^'vi ocHi d\-^ ON <-*v>j
19
fcs)\0 COOs*-^ 0^^ O'-^*^'^ 0000
CO U CN*^*-^ N^ U 06-4^ lN»
P3
' VH fej M -^ 4k -fi. -^ 4^ -^ v-a ^
K-^wi\^. \iv^ t-4w» O"-'-* ccOjjC
0(
M to hJ U^ v**^ v*j oa .^
Wl M 4^ tJ Ovt ^ VK>
1^
•-• ^ tv) tj N> K)
M 00»-w xOO lo-wi o»^
00 OD VI 006
?
>:
1^ 1^ H>« »M
^ VO u* 0\^ 00
V^ W M 4^ fc*
vq \^ Vx v-i N^ 00
•
~00K»O\ O^.^N4^v^
M 1-4 s>4 4^ 4^ ls> '
TAB L E
o t
Artificial Sines
AND'
TANGENt-S
to
every
1 «
Degree and Minute
o F T H E
OUADRANT.
The CcmmomRdJUm i^ifUg lo^ cooooo.
L 6 Kt D O Nr
i^finted in the tear MDCLXXVit
B - -'■
■ Degree o.
■ I I I ■■ ■ n I I II ■ »
Ml Sine | Co-fine \ iTangcntj C(htang
o| 0.000000] to. oboooo) 1 0*000000 1 Infinita. \6o
I
1
J
4
5
6.46 37 z^
6.7647^6
6.940847
7.065786
7«i6i696
9.999999
9.999999
9*999999
9*999999
9-999999
6*46ly%6
6.764756
64^40847
7«o65786
7.161696
7
B
9
10
7*^41877
7.508824
7.566816
7.417968
7.465716
9*9^9999
9*999999
9*999999
9.999999,
9,999998)
l7.*4i878,
4.508825
7.566817
7.417970
17.465727
II
14
7.505.118
7.54190^
7.577^68
7.609855
7.659816
16
17
18
t9
20
9-99999^
9.599997
9*999991
9.99999^
9.99^996
7.505120
7.541909
7.577272
7.609857
7.6J9826
7.667844
7.^94173
7»7*^977
7.741477
7.7^47 U
9*99^9^
9*99999^
9*99999^
9*9^999^
9.999995
2.667849
7.694179
7.719005
7.742484
7.76476^
II
22
14
25
7.785943
7.806146
7.«2545i
7.861662
9.999992
9*99999^
9*999990
7.845934 9*9999^9
9.9^99^9
7.7859511
7.806145
7.825460
7.8 4 J 944
7.86t67'4
16 7.878695
7(7-«95o«5
*8 7.910879
?o
7.940842
9.999988I
9.999987
9.9999^^
^9 Ti^ity - 7*7179^ ^ 7«^i^«54
9-999985
7.i{787o8i
7«89l099
7.910894
7.940858
5.536274
5.255244
5.059155
2.954214
2.857304
2.758122
$.691175
2.655185
2.582050
2.55^175
59
5^
57
?
54
55
5i|
51
50
2.494S80J49
2.457091 48
2.422528 47
2.590145
2.56oi8o'4f
46
2.552151I44
24505821145
2«28>I99fl42
2.^57 5 16] 41
2.255259I 40
37
2.214049
2.195845
!• if 4540
«l^.i56o56
2.158326 55
l^
2*I2I292|34
t*xt>49^ 33
2^089106 32
ft,«73«^4 gi
2.059141 30
I Co-fine I Shie*' {Kio-tam. fTangentlM
■U3grfle8j>. ..
T
■>.
o^
M) Sine- I Celine- \ ■ riangenti Co-tang. \
30l7.94o84i'9.99y9gj) |7.94oBt8Iu.o^9M
7.95^o»i 19,99998:
7.9688^09.99998
7.98*13} 9.9999S0
7.995138 9.999978
g 007787 J 9.999978
1.044900
.1*17747
: 1^0 47^1
'•9»"9I
8.04'iSo:
8.0(478
1 1 9.9 99976
9-999971
9'99997i
9-99997
9- 99997
ioo44Ji»*9/9956
8.05194? 11.968615
8.o4J5*7 i'^)**??
B,oi48o9 11.^4 ft*
lB.o4l«o6iii.9I4J94
1.07*500
.086965
.09716 J
.107167
.11691*
9.999969
9.999968
9.9999616
9-9999^
9.99996 ^
i».07*il>tii'9»3469
B.<3«6997 JI.91J00J
3.097 117! 11.901783
3.jo7iojri (.891797
8.ii«96?lil.88j9j7
e. 11^47
8.«i5Bi,
44? 13
...51907 .
8.i6i68it.
9.99J959
9.9999 it
9.99995S
18. 116510
8..J585
1.14499*
»-'5j9J
|8.,6i7j7
B.171180
3.1 7971 J
53l6.i879«5
5*«.i96iot
55^8.104070
9.9999i-
9-9999^*
9.999948
9,999946
9-9999i^
1895
8.«7IJ4
ll..7ijti
I.i797«5
I.l88a!.£
9.999941
9.999940
9.9999^
9^99991^
9-9999i9
■ i9il
.964'
L7195
|8.ij46t
4T?«
"■87J49'
i.864i49
1.855004
1.34604*
i.aj7iTi,
:i;3i867-
ii.SioiJ;
11.4(1964
.8o}t.
;T9I<r4
: 1:7 88 047
.1.7M05
'7<5!T9
;|€#^iwJ_| Sine |- lC»<j>g.j Tangent ^M
DegeeS
Ml Sine .\ Ca-fini\ iTangoitj O-tittig* (
Degree
I.
f
olS.ii^i855l9.999954|' |8.x4i9iM
ir8.z49pj5
x[8«256o94
8.263042
8*2698^1
8#2766i4
3
4
J
6
7
8
9
10
9*9999 m
9'9999^
9*9999^7
9'99V9^S
9.99^21
8.249102
8.2^^165
8.2631 15
8.269956
8.276691
8.28'^24;
8*289775,
8.2^6207
8*^02546
8.J0.8794
9.999920
9.9999x8
9*9999 ^^
9'9999H
9*9999^o\'
^•28. 3 323
8.289856
8.296 292
8.3^2634
8.308884
12
H
£5
16
»7
18
*9
zo
8.^21027
8.327016
8.J?87lg
9.999907
9.999905
9.999902
9.999899
9*999^7
8.315046
8.32II22
8*3'27ii4
8.333025
^.338856
8.344504
8.350180
8.355783
8.361315
9.166777
9'999^9^
9.999891
9.999888
9*9998.85
9.999882
8.344610
8^350289
8.355895
8.361430
^•366895
2I(
22
L
231
i4
26
28
^9
8*372171
^•377499
8*3827629*999873
8^387962
8,^93191
9.999^9
9.999876
9'999ho
9*9998.67
B. 372292
8.377622
8.382889
8*388092
8-i93i34
8.598179
^•4<^J^99
8,408*61.
^•4«79^
9.999864
9^999?$l
9.999858
9.999854
9i»99985i
8.398315
8.403358
8.408304
-8,4^33.13
8.418068
.758079160
.750898
•745831
.73^8^5
•750044
•7*3 3P9
59
58
57
561
in
54
53
.716677
4716x44
.ro37o8J5i
.697366 5 1
^VJrl6 50
•6<J49-54|49
.678878 48
672886 47
.666975 46
.661144(45
•655390144
,649711 4j
.644105 4>
.638570 41
.633105 40
•627708
.622378
.617111 37
•611908
.606766
39
58
3^
35
.60x685 34
^^^666% ^ J
•591696 3 2
• 586787I31
.581932
5Q
If
, Pe grce 8g. '
iJBumuaug ?
.1
m^
37?*45044O
38 ^,454?^^
$9 8.459^01
2|40 8*4^36^^
I
^i«Ma«pi»
Degree
I.
Ml Mm I C<hfme\ ITangentl Co^tang \
^mi^" I ^ — »— II - -— — — > II ■■!■ ' '- III I I. II . .
5o|8»4i79jat9.99985i[ l8»4i8o68jif.5Bx93iJgo
8.411717
8.42746<i
8«4J'»i5^
; 518.4413^4
I
I*
5?
9.999848
9.99P844
9.99984,1
9.9998 J 8
9.9998 H
8.411869
9.417618
8.4^1315
S.436961
8.441 $60
1.571582
1.567685
M^3Qj8
1-5^8440
9.9998} I
9.999827
9.999824
9.9998 lor
9.999816
i
8.446110
8.450615
8;45^070
8.459481
8.46J849
8,467985
41
41
43 8-47^49?
44 8«48 069^5
45[8«4M48
47
48
9'999^M^
8*47 »»^3J 5^-9^98^9
9'999^of
9.999801
9.999797
8,468172,
{•47*4f4|
•47669^
1.4808911
♦•485.0501
49
Jo
8.^88963 9.999794J
^•49394}> 9*9%9i9o
S»4*Z97A 9^9997^.^
8(.5o^o8o 9*9997^%*
8.505045 9'9997t^'
8.4891,7b
M93*5?
N97*9J
8*501298
P.J05167.
5-1
5a,
5^
^•50897419.999774
►5xa.8f7
^Ji^J^fc99M5
iJ54[8tJ>Q}ff
5? 8*524341
P-^997^9'
9.999761
9'99975^
i
i 8^ 509160
56(8. 5 18 idiJ 9.9997 53 n
57 3-5ji$28,9^999748;[
8j5j9j8^ ^,999740
. ••5*9!799]M*4W%J?i
■ ffc.5245 ^^1ta,47j4H;
^^'—*^^ ' '» ««».ii.i.ii ,<»^__,_____—
.^9
28
2$
a5
i'55399o 24
1.549387 ij
1-544930 12
1.54^519 2J
1.53^151 10
1.JJ1818
1.52754^
i»5i3J07
1.519108
»'5>495ip
18
17
16
Vn5?3^i
Jti5oi797
^!49»879i
^;49473:3
14
12
il
i
1.490899
i-.4?$9Pl'
1.4*3^3^
.'S
.8
V9
60
?:i42i?f 1 ^99mH I '^^43:0.^ 4
8*5183.4911 1.47 \^
J.5I,io?c^ 11.4^^0
Hip 79 1^*454^?
?»f39;447l"»49P553
11.416916. jjp
*— ff
B3
Deg tee aT*
Ml . Sine ~ Cir^iite \ (Tangent |-C»^ct^. |
8.;4i8i9,9.ggp7 3j
9-9997**
?-9P9ni
9-5?97»7
9'9997*3
■ 8-(499P5
I 8.iJ7*U
'**J?{^.9'99Pr«'^.
6.^^4114 9.399694
6,^874*0
i7J^«o6m
iB|«-ifidj48B
P.99?**5,
p.99$(!»6;
9-99P^h
P-99J8t!' ,
p; 99^546'
.J4669itu.45Jio9i59
8.1^1817
B.5I7!!^
G.i[£oSi7
IB. 164^9
M7"!r
^.* 74**0
JM77877
?lf«7?9*
•44?7^i 58
.'.44«t8j S7
Mj*7t'S'IJ4
■1.41111 J
11.41^486
■ i.4tiio5
li||«/iS»i3j^.999fM
ti!5rfirt9i f.999^29
l4|8i(Sij^7]ti99^
8.^^i^ 9^.j9^rf)
BSff^M?.9>9j^7
B£< J«y 76 9.9^5.9 1
«r«|44j^i't;JiJJ74.
[t.'«j7iSriri';J5i8ii
■-'•feeg'efc^?.-.
Degree!. 1
■
Mt Sine I Cn-fine 1 ll'angentlCo-fMjr. 1 |
50«!9<7jl9.999!!61
[8, 6^00? J
"■J59907ljcl
I>
•.«4'9'J
8.64*981
•I.J57017
:«
«.<494.i
S.«45a5}
1..3S4147
t!
!.<4S"74
9-999170
I.rf48704
11,351196
8.«9i.o,
fe.tfiiJjB
.1.348461
ti
!
S.69J911 9.999998!
8.(!j4IU
U.J41M
1'
?«
8.596701
9-993^5
1.657143
II. 541851
1.
:7
3.699479
9-999U7
8.<Si99»8
|8
8.«««,o
9.993)41
II-3J7J11
11
!»
e.««4968
P-9SI9IJ5
^tfr?'
ii.jHiS?
M
40
9-999 1^9
11.331840
^
41
B.670J9;
9-999iii
8.^76869
11.319130
41
8.<j!o8o
j^99Ii8
M7!9'J
1 1. 3 164 J 7
41
8.<7979l
5.999JIZ
8;«7«iJ9
11.313761
17
44
«.57«40'9
P.999J06
8.678199
1 1.5 i 11*0
>'
4^
8.681041^.959499
8168 !S44
"-.118456
M
H
4'
8,68^6^5 9.99949J
^.684171 ii.)i98ta
47
e-.«8«i7. 9.9994»7
B 6784 11.JIJ116
M
,«
8.68,889.9.999481
f! :9!<i ir.JibSiil
49
S.S9i45« 9.999479
f .196! I..!o8o!7
Jl
So
8.69J998 9.999465!
" J4:5isli'.Jo947i
',»
91
".69694!
8.697081
n
8.69907J
<i.99?4iS
8.699617
ti.'!oo3«3
-
<:
8.70it8;
9-9994!o
SjTbii!!
r..t97»6.
9'
f'T'2
9-99944 J
8.Vo4«46
ii.tgiBfo
9!
8.706176
9-9994J7
!.707i?9
_J
4
9<
8.709049
9-9994 J-I
B.JO96.8
11.19^.381
9;
8.71190:
9.999414
8.VII08:
11.187917
■
91
l?Ml',
8.7I4SJ.
I
9»
8r7I«97»
ii^iB'joil
1
So:3.7i!* 0019.3994^4!
8-71919*
11:180604
[Clzfiii 1 Sinc'l JdMOT^.lTaBgelitlW
... Degtee 8r.
B +
Ml Sine \Qo^tne J lTangcnt| Qhtdng. ]
ol8.7i8Bool9.9>94^4l 18.7*959^1
9.999 3 98 1
9-9991^4
8,7 11^04
^7x3591
3 8.7^5971
48.728??^
518.7^0688
9.999 J 78
9.999371
7
8
9
16
II
8.73 goi7
8.757667
8.7399^9
8.74x159
9.9993^4
9-999357
9-9999 50
9-999J43
9>99933^|
8.71^806
8.7*43^54
8.716588
8.718959
8.731317
8.735663
8.73599^
8.738317
8.74o6z6
8.741912
8.744536
i2f8.7468oi
8.745955
8.75l»97
8.7535x8
K3
M
H
16
17
'9
16
9*9993*9
9.9993 *it
9999515
9.999308
9.999301
8.745107
8*747479
8,7^9740
8.751989
8.754117
8-755747
^•757955
8.7^9151
8.761337
8.7645x1
9.999*94
9'9?9*«^
9-099*79
9*999*7 1
9.999116.5
8^756452
?;7.S3668
8.760871
•8.763065
8.765146
X4
11
*3
24
»5
8.766675
8.7i688i8
8.77097^
8.77 3 10 1
.8.775*13
9.99?* 57
9-999*4*
9-999*3 5
9.999127
*^}?-7f73 33
*7 8.7794i4
2M.78^5>4
*9 8r7?3^Q5
3^^8.78 5*7 5
9.99^120
9'999\^^
9*99Si*o4
9*999^^97
9*999^^9
8.767417
8.769578
8.7717*7
8.773866
,8.775995
8.778 114
?.783iii
S.782320
-784404
.8.786486
.180^04! 60
.178194
.175796
.*734i»
.171041
•168683
.166357
•164004
.161683
•* 59374
.157078
S9\
y8
$7
Si
53
5*
51
5X3|
.*54795
.*5*5aj
»1$Q14.0
•14801 I
.*45773 41
49
47
46
*43547U4
i^*4»J3*4i
.119118 41
.*J^935 41
.*347.Hjg
.39
38
li7
3*
35
34
33
.131583
.130411
.^18273
'.*i9i34
.114005
•111886
•M?778 _
.117680 31
,1^549*131
L^
I'Corl^S^ \\ Sin^ 1 iCi^tang. \ Tangfent |M
Degree »<i. - "
I i ll! Il t^rf M l I 1
« f
.1
Ml Sine I Qhfine | iT angentI Co-tang. |
go '8.78 567 5 19.^^9189 1 I8.786486
» I . ■ ' II- " '
34
61
17
40
8.787756
8.789787
8.791828
8.79J859
8.795881
9.5^^174
9.9^166
9.999158
9.999150
8.788554'
^.790615
8.792661
8.7^4701
8 7967 J 1
V^785?4
^•799^97
8.801891
8.^03876
8.805852
9-99914*1
9.999134
9.999116
9.999118
9.999110
8*75(?7Si
8,800.763
8.802765
8.807458
8,8^6741
41
41
43
♦4
4J
46 8.8 17 5 111 9.999061
S«8i94j6 9-999o5i
3.811 J4V ^ ^
8.8 1^140
*7
48
8.807819
8.809777
8.8iL7i6
8.813667
8.815598
9.999102
9,999094
9.999086
9.999077
9.999<>^9
8.808717
8.812683
0^81:^^41
8.814589
S.8 16529
A9
50
8.8
Hi
9*999044
^,.99903 6
^^
9.999027
M 1846 I
8.820^84
8.8222^8
8.824205
8.8241^3
8.827011
8,82818^
8.830749
51
U . ..
54^1x106^.998993
8.83445.6
56 8.836297
57 8.838130
58 8.3j9^56
59 8.841774
,6018.84^5^.$
9^999019
9.999010
9.990001
9.998984
3;? X7 9^1
8.819874
B.831748
M .3 547 1
9.998976
9.9985^7
9.998958
9.998940
9»»9§894i
8.837321
8.83.9163
0,^40998
8.841815
^•844644
*i35i4i36
.111446
.209387
.207338
.205299
.^03169
29
28
»7
26I
*20I248
?^95fi37
•197^35
.195*4*
»4
»3
*i
.193158J20
.191x83
.189317
ji^7359
.18^5411
.183471
191
X
16
If
1.181539
,179616
.17770X,
17^795
.1738^7
«4
1
XjO
.172008
.170X26:
.168252'
.166387
i.i6452$l
*« ■ J - ■ ■
7
6
5
•162679I 4
,160837 3
.159002 i
.15717S X
■ ■ | - I I ' ia I I I " I 1' I I I - -
[Qhfine I Sine t i Co-tan^. J Tangent lAf
Degree g5» ;
'•' «» « «
--._ *.t-
Lk
lTangent[ C9-t«ig. 1
Ml Sine ICo-jMt
• I«.»4!!«4i5-95«94«l |8-844«44
ii.iS5!561«o|
i 8.84^87 9.998331
.846451
.'-.!!545
5f
• !.a47i»!
9.99891J
11-151740
(■
J S.848971
9.998914
.850057
ti-'4994!
(7
4
8.8T07T1
9.998905
■1-.48.54
56
J
8 «!.!>!
9.998896
li,.4«!7.
55
54
6
!.8l4>9i
9.998887 1
-85540!
■...44597
7
83)<o49
9.998878
.85717.
.!.. 41819
<1
8
8.85780.
J.99886J
.8589!.
11. .41068
5.
9
8.8S9S46
9.998860
Ii.ir9!14
51
id
8.86ii8j
9998851
.86.4!!
■■.■!7!'7
5.
II
8.8«!o,4
9,9988,1
.864.7!
ii.i!l8.7
45
11
8.JS47JS
9.998!!!
4I
«.8«6,(,
9.9988.!
.86763.
....;.!6!
14
8.SM.6S J.99881!
.869,5.
....!d645
41
IS
8.8^986819.998804
.871065
.....89!6
45
16
8.87>i6!
.87.750
11. 117. 30
44
17
8.87J1I!
.8744*9
i.:i.5(!.
18
8.874958
9.998776
.87616.
ii.i.j!!!
4.
19
8.8,«6n
9.99«7«
.87784!
ii:tiiI5i
41
8.S7l.lr
9-998757
■879S.9
....10471
4t
!1
&i
8:879949
9-998747
.881.0.
... .18798
i>
8.8ai«07
9.9987J8
7'i.*l7.!.
!«
>l
8.S»J!!«
99987*8
.«84<?o
<M1!470
!7
>4
8.88490!
9.998718
.S86185
...lijSis
!l
1*
8.886541
9.99B708
.8878;!
.J,....«7
!J
!4
f«
8.888174
9998699
.889476
11.1105.4
a7
8.S89801
9-998689
■.B„iii
:i.io8l88
!!
.8
8.891411
9.998679
■89174.
ir.I07.58
u
19
8.89JOJ5
9.998669
.8,4j»6
M.105654
^1
>"
8.l9,i,;
9.99«6!9
.895984
J..JO40.6
!o
■ j£.-/"oie|_Smc f ICk-mj.
'Tangent
m
. .. , ., DcBiec 85. . I
(Degree 4,
Ml Sine f Cihfine I ITangcnti Co-ian^. \
-f»
JO 8.8941645^9.9986591 18^95984
8,89^246
8.897«4t
8.899^31
8.9616!^
8;96if96
9.098649
9.998619
9. 9986 1 9
9.998609
^9
140
8.904169
9.998599!
8'^^7 5^ 9-998589
8.90^197 9998577
8i9d885 J- 9.998568
8i9ip404Jp.998558
8.897596
8.899105
8.900803
8.90259^
.8.903987
1^90557®
5-907147
8.90^719
18*910185
. 18.91184^
4118^1 I949J 1^.998 548
i'l 8.913488 ^998 5 37
43 ^.-945011 ^^998517
'44 8,.9i 65 50 ^1998516
^5 ^*9^807its.998 5o6
?;9IJ40I
P:9i495i
8.^16495
8.918034
18,919568
4'^{8.^i9^^f9il9^.9984Q5|«'
47 8.92^"03 y.998485 ,
48 ir.92'i^ib 9.998474 '
49 8;924fii b.998464
ijft 8.9i7Jotu.998442
5*8.9^^^871^998431
^3 Sipjd^B 9.998411
54 8;93i544 9.'998'4io
8,921696
8.922619
^.924136
$^925649
8"927i56
^.9281658
t:93oi55
r.931647
^-r — ^5* j^i-ij y.yyo^xvi «.93Jl34
in8:9iiP?jy^^
5te|8,93448i ^.998?88 3. 936093
S.9375«5
?'.939o3i'
.940494
^7
59
o
. mm
8.9j448i 9.^98388
8.935942 9998377
58 «^3n98
f.^ 98 366
8:5^3^850^:998355
? 9^4^-^9^1^119983 44] )A^4 1 95 1
'io40i^|3d
.102404
100797
.099197
.097602
.09^013
It
16
if
.094456
.092853
.091181
.08971$
.088154
2Q
— .-(
.08659^,
.085049'
.©8350.5
.081965
.o8Q4J52ii^
161
;0739^4
.077^81
.075^^4
.074351
.07284.4
14
I2
It
10
9
.071344
.0698 4 J
.068353
.065.^84! S
I
.06 3 907 yi ,
063.431 "
.o6o;^8
.059506
.05^8048
1
I
1-jCtNt^ j.l Sine I \Cortang. \ Ta ngent
. ^ •■ -Aw* .«4 _ .
Degree 85..
M
Ml Sine {Qhfine I ITangentj Ct?-f ^gp I
olS.940296 19^998^441 18.9419^1111.0^8048 |6d
Degree 5.
1J8.941738]
8.944606
8.9460^4
4
5
16
7
B
[P
^o
II
^
14
;^5
9.998333
9.998311
9.9983 1 1
9.998 300
9,998289
8.943404
8.9448 $»
8.946295
8.^47734
8.949168
8.958814
8,950287
8.951696
8.953099
89^4499
".05659^1 f?
11.051148
ii.o5.J7P5
ii«o5o83t.
9,998277
9.^98 266
9-998*^5
9,998 24 J
9.998232
8.950597
8«952oii iir047979
8.953441
8.956267
11.049403
1 1.04^5 19
8.954856 11.045144
Ji.0437?3
^.955804] 9.998220
8,957184
8.958670
8.960052
8.961419
9,998209
9*99^197
9.998186
9.998174
8.957674
8.959075
8.960473
8.961866
8.963254
11.042316
IX 040915
ii,o39527
li.o38i34|4^
11.03674^4^
j6 8,962801
17 5.964170
i» 8.965534
9 8.966893
20 8.968249
-1*
I
12
n
n
8.969600
8.970947
8.972289
8.975626
8.974962
9.998163
9*998 151
9.998139
9.9^118
9.99810^
8.96463^111.035361
8,966019 11^33.981
8f967394 ti,c^3i6d6
8.968766 11.03x134
8.970I33I 11.029867
44
H
4*
4?
4C
9.998104
9.998092 •
9.998080
9.998068
9.99805.6
8.97i495(x*.q2'^~5o5
8 97*855 11,017145
8.974109 Iii0f579«
8.975560 fj.a2444P
8.976906) t>i«Oi>3094
26 8.976293
^ 8.977619
28 8.978941
29 8,980259
8.981573
9'99 80.44
9,998032
9.998q*o|
9,998608
9.997996
- — ^- " - —
8.978148
8.97.95,86
8.980921
8.982251
I8.98J577
» 1 1 I *
19
J?
i
li.o;ji75i
11^020414
11.0L9079
11.017749 3 «
11,0x6413 go
34)
33]
3*
^
' I ' ' > ■ ■. , .., — - . ^
r Co-fine \ Sine ) \Co-tang. I Tar^ntjM
^""Pegree 84-
Degree ^.
Ml Sine I Confine \ Tangent | Co-tang. I
56|8.98i575)9-99799^t \^*9^Z^77\^^-oi6/^%^\^o
8.984899
8.986x17
8.987^3^ 2»
a. 98^^841
^.990149
8.98188519.997984
8.984189 9.9197971
8.98^491 9.997959
8 986789 9*997947
8.9880^519.997955
5»
?4
!5
^618.989574
3718.990660
58 8,991945
59189951x8
4o|8,994497
11.015101
11.015785
11.011468
11.0111:58
11.009851
*9l
i8
»7
16
t5
8.995768
8.997056
8,998 19^
8.^999560
9.000S16
9.9979*1
9.997910
9.997897
9.^97885
f.^9787?
8.991451
8*99*750
8.994045
8.995537
8.996614
11,008549
11.007150
".005955
11.004665
11.005576
»4|
*5
11
II
iM
4»
41
4S
44
45
9.99^860
9^^97847
9.997835
9.997811
9.997809I
.[8.997908
8.999188
9.000465
9.001758
9.005007
11.001091
IS. 0008 11
10,999555
io;998i6i
10.996995
»9
18
17
16
15
4^
47
431
49
9.001069
9,005518
^.004565
9.005805
9-997797
9.997784
9.997771
9.997758
9,004 1 7 il 10. 99 5 7 18
10.994466
50I9.007044 9'9977?i|
9.005^534
9.00679^2
1 9.008 047
I9.009198
10.995108
10.991955
10.990701
14I
11
XI
101
5119,008178
51 9.00951^
55 9«oxo757
5419.0 11961
9.997731
9.997719
9,997706
9.997695
19.0105461 10,989454
5 5 19.01 5 181I9.997680
9.011790
9.015051
19.014x^8
I9.015501
10*988110
10*936969
10.985751
10.984498
9t
8
5
S7
5»
55>
9«o 143 99
9.015^13
9.018031
9.019135
9.997667
9.997^54
9.oi68i4] 9.997641
9.997618
Q. 997614
9.016751
9*017959 10.981041
9^019185
9.010405
i9.oii6io
0.985168
10.980817
10.979597
10.978 5 8o|
I
01
r Qhfim I " Sine I I Co-tang l Tangent | M
^■PMIK
P«ree 8
.VirfM
Degree tf#
Ml Sine | Qhfine I |T^gentl Ca-tang.
o|p.oi9i35l9*p97^i4| |9«o%i6so| 10.978^80
■I ' ' " ■ '■' " ' ' ■ 'I i"^— .
I 9.010435
14 9.024016
f 9.o25»oj
9.997661
9.997588
9*997 i7^
9.997561
9.997 548
9.021834
9.024044
9.025251
9.02645 5
9.027655
10.977166
10.974749
^0.973545
<o.97^54 5
9.026386
9.027567
9.628744
9.029918
019.031089
6
7
8
9*997 S^^
9.997520
9.9^7^07
9^997493
9.997480
9.028852
9.030046
9.031237
9.032425
9.033609
9.032257
9-03 34* «
9.03458*
9.035741
9.997466
9.99945 »
9.997439
9*997^^^
9.9974"
9.054791
^.0359^9
9.037x44
9.038316
9.o?94«5
7
8
9
20
9.038048
9.039197
9.040342
9.041485
9.042625
9*997 S 97
9*997 3^ ^
9*997 $^9
9-997355
9.997541
9.040651
9.04x^13
9.042973
9.0441 30
9.0452*4
z
2'
4
i5
9.0437^*
9.044895
9.046026
9.047 1 54'
9.048279
9.997327
9-99731?
9.997299
9.997285
9.997271
1 9.04643 4
9.047582
9.04^717
9.0498!69
9.o5tQ!g8j)[<y.94^^92
%6
%7
28
29
50
9.049400
9.050519
9.051635
9.997256
9.997241
9.997218
9.05^749 9.99^ *»4
9.0538599.997100
9.052144
9.053277
0.97 1 X48
0.9^954
0.9^87^3
0^7575
0.96^391
0.965209
0.9^403 1
0.962856
0.96x^84]
0.960515(4
<^.959349l44
0.958x87 43
0.957627 42
0.955*70 4*
0.95471^ 40
0.953566
0.9524^8
0.951273.
0.950x31
39
38
3^
i
0.94^856
0.946723
*Co*fpte ] Sine
9.05440^ 10.94559*
9.055535 P<^944465
9.0 56640; 10.94 3 3 4o[ 3
Ci^jmfr. iTangertt]
■MUOM
-C^^ ^3
c
Degree 6
{Ml Sine I C<hfine I |Tangent!Co-fif/!g.)
?oJSf.o$ 585919.997 1991 i9.oS6^4ol
51
Si
S3
9.0 J 49^^
9.056071
9»o57i7»
349.058271 9.997141
S5|9*o593^7 9*9971*7
S6
9*997 18 5
9.997170
9.997 M6
9.057781
^•058900
9»o6ooi6
c.o6ii}o
^.o6»x49
37
38
9*060460
9.06 15 5 1
9.06x638
S9 9.0^3713
40 9.064806
9.997112
9.997098
9.997083
9.9970681
9.997053
19.063348!
9.064453
6,065556
^.066655
9.067752
4»
41
43
44
45
4"^
4i7
48
49
50
9.065885
9.06803.6
9.d6js^i07
9,070176
9.997039
9.997014
9.997Q09
9-9^994
9.996979
9.06884^7
^.069938
9.07 ix>i7
9.0721 1 3
^.0731 97
9.071242
9.072.306
9.073366
9-07 44*4
9.075480
9.996964
9-99^94^
9.996934
9*99^9^9
9.996904
9.074178
9.075356
9.07 64 3 i
9.077505
9,078576
51
5a
53
54
55
9*076533
9.077583
9*078631
9.079676
9bo8o7i9
56 9.08175919^996812
^^96989
9.996874
9,996858
9.996843
9.99^828
57
59
60
9*o8»797
9.o8383;2
9.0^4864
^085894
^996797
^996782
9-9967^
9.996751
9.079644
9.0807 10
9.081773
'9.082833
9.083891
0*94334 01 3c
0.942119
0.941X00
0.939984
0.938870
0.937760
28
17
16
0.936652
0.9355+7
0.934444
0.93 3 «45
0.932248
^4
22
21
20
<^.93»i53
0.930062
0,928973
0.927887
0.926803
19
18
17
16
«5
0.92572a 14
0.924644 13
0.923568 li
o«9j^2495 XI
0.921424 lol
0.920356
0.919290
0.918 £27
9*917167
0.916109
9
8
7
I Ce^mt I Sine |
9.084947
9.085999
9.087050
9.088098
9.08914 4^
yCotang. I Tan geiitiM
0.915053
0.914000
0.912950
0.911.^2
0.910856
4
3
2
1
■*i«
Degree 8j
. ^ Degree 7
M| Sine 1 Co-fine I ITangeitt {Co-tan^. \
p| 9.o8 5894 9. 9967 ill j 9.X)89i44| 10.9 1 o)^ 5 ^ i ^o
I
2
5
4
5
1
8
9
10
II
12
^4
M
9.086911
9.087947
9.088970
9.089990
9*091088
9.9967 J 5
9.996^10
9.996704
9.996^88
|9jD90i87
9.09 1 zi8
9.091166
9.o$?35oi
9.094 J ?6
10*9098 1 3
io.9oS77i
fio.907754
10.9066^8
10.90^664 5
9^091014
^093037
9.094047
9x^9606 1
9.996657
1^.996641
9*996625
9*996610
9996594
9.097065
9.098066
9*099065
00062
^105^
9.
9-
1^19.
17I9.
18 g.
»9
20
9
9.
9-
II
12 9
»4
15
9.
9.
9.
16
18
9*
9'
9'
9'
9*
9,996^7%
9.996^61
94996^^6
9-99^ Sio
9^996514
9.095367
9.P9^395
9.097^412
9*098446
9.099468
10*9046^3
10.903^^604
10,902178
io;9oi5f4|5xj
10.9005321 5(
9.100487
9.101504
9.1035^2
9*104542
10.8995 13 j49j
10*898496148
9.X015 19 10^897481(47
1 0^896468 14
io.8954W4f
0^048
03037
040 2 J
05010
0599*
9.996498
9.996482
9.996465
9.99^449
9.99643 g
9.*o555o
9.106556
9.ro856o
9.109559
io.«9445o
10.893444
9.107559 10.892441
10.891440
10.890441
44
4?
4M
4'
4d
06973
07951
08927
09901
10C73
9*996417
9.996400
9.996384
9.99^ ^U
9-iio,556
9.i"55J
9.11254?
9"55J3^
9.114521
10.889444
10.888449
10.88745^
10.886467
1,0.885478
11842
12809
J?774
14757
1^698
9-99^3 3 5l
9.996318
9.996302
9.996285
9.996269
9.ii5507hio.8t4493
9.1x6491
9.117471
9.118451
1^9.1 19429
10.883509
10.881518
10.881548
108P0571
I I II. ■■ I ■ ■ fc > II «< ■ ' ■ ■ f — m 11
[ Corfine I Sine | lCo^<«5g.|Tangeotl
Degree 82 '"
-iMMM
. . , Deg ree 7>
Ml Sirie \ define \ [Tangent | Co-t<g/?g, |
5019.1156^8 1919962691 I9.1 194x9)
o.38o57i'3o
J 1 19.116656
[Z 9.117611
4
5
9;ii8567
9.xt95i9
9« 1 1046 9
9*.99^il^
9.9961 1 S
9.9^6101
19.996185
9.110404
9.111377
9.12134^
9.1255X7
9.124184
19
iS
o;87^596
0.878623
0*877651 27
0.876683 16
C.875716 15
7
S
o
9;iii4i7
9.111^61
9.12^0^
9.124148
9.115187
9.996168
9.996151
9.996134
9.9961 If
9.996100
19.115148
9.1261x1
9.117171
9.118130
9.119087
0*874751
0.873789
0.871818
0.8^1870
0.870913
14
It
11
10
1J9.126115
9.117060
9.^179^1
9.129915
9.119854
9.996083
9,9^066
9:996049
9.996031
9.9960 1 5
9.130041
9.1309I94
9.13 1944
9.131895
9.133839
0^869959
0.869006
0.868056
0.867107
o.8^6j6i
\9
17
16
9.130781
9^131706
9.131630
9M5J5I
' 9' ' 3 447 ^
9*99^99^
9.995980
9-9959^3
9-5^9594^
9.995918
9154784
9-»J^7*^
9.136666
9-1 37^0 f
9:i38f542
0.865116 14
0.864174 13
0.8.63334 ii
o.M%i9$ IX
o;^6i458|iQ
|9.i3 5387l9.9959ii[
9.136303 9.995894
9.1 37*x6 9.995876
9.138.127
9.1 3^37
9.995859
j^.9958^1
9.^?9^7^
9.140409
9.141340
9.14226^
19143196
0.860,514
0.859591
0.858660
0.857731
0.856804
9i
8
7
6
5
9'i 19944
^14085-0
p.141754
9.X42655
9.995825
9.995806
9.995788
9-99^770
9.995753
9.I44121
9.145044
9.1459^5
9.1468^5
9,X478q5
0.855879
o.85495d
0.8.54055
0.853115
o;852i97
4
3
2
I
01
Co^t \ Sine I iGo-^iiwg. t Tangent JM
Degree 82.
e
' Degree 8.
Ml Sine j Qhfin e ( lTang e nt| Co-f^g ^ I
ol9.i45555i9-99S755l |9:i478o||
I
2
9.I444S3
9-»4«49
J 9.14^*43
4 9'»47M6
5 19. 1 48016
9-995735
9«9957i7
9.99568.
9.995664
I9.148718
9-149^ S»
9.1S0544
9-MI454
9.15x363
7
8
9
10
9.X48915
9.149801
9.150686
9.15x569
9151451
9.995646
9.995628
9.995610
9995591
9-99557?
9'^U^^9
9.154174
9.155077
9.15597S
9.156877
hi
12
14
X5E9.156830
9.M3no
9.154108
9.155082
9'^^^9S7
9-995555
9*995537
9-99^ ^^9
9-995 5ox
9.995481
9-»57775
9.158671
9-1595^5
9«i^o457
^^161247
16
17
18
19
20
9.157700
9.158^69
9.15943^
9.16030X
9.995464
9.99544^
9*99542'7
9.995409
9.161164 9.995390
9.162236
9.163123
9 164008
9.164891
9.165773
2.1
22
»4
15
9.;62€a5
9.162885^.995353
9^^6374^
9.164600
9.1^5454
9-995 37*
9.995 33*
^.^•95316
9.99 5297
9.166654
9.167532
9.168409
9.169284
9.170'! 57
26
>7
28
»9
o
91.166307
9.167158
9.168008
9.168856
9.16^701
9.995278I
^.99526©
9-995*4 1
9.995222
9995103
9;171»29
9.171899
9.172767
9*i73^34
9-174499
0.852 197 |6c
o.85ii8 2
0*850368
0.849456
a84854.6
0.^47^37
59
58
157
56
55
0.8467^1
0.8458*5
0.8449?- 3
0.844022
0.843122150
54
53
5a
51
0.842225 49
084x329 48
0.840435 47
0.839543146
o>838653{4f
0.837764I44
0.836877 43
0.835992 42
0.835108 41
0.834226 40
0.833346
0.832468
0.831591
0.8307x6
0.819843
39
38
37
3^
35
0.828971
0.828101
0.827233
0.826366
0.825501
34
33
3>
30
{Co-fine] Sine I \Co-tang. \Tzugcnt \U
Degree 8 1,
-nr
' Degree S;
Ml Sine I Cc-fitte I tTaiigentl Ce-tangk
{019.1^9701 (9«995^o;^| 1 9.
Ji;5^.i70f46
54
IS
9,X7ij»9
9.171250
9.175070
9.173908
9^995 184
9.995165
99^^^^
9*99 U 17
9.995108
9-
9-
9.
56l9,i74744
J7l9'i75578
5819.176411
5919.177242
4019.178072
9.995089
9.995070
9.995061
9.995031
9-99 50.11
9«
9-
9-
9.
9.
41
41
45
44
45
4<i
4^
48
49
50
9.178900 9.994993
9.179726
9.180551
9-181574
9.181196
9.iS5oi6
9.185854
9,184651
9.185466
9.186180
99^4974
9^994955
9-994955
9.994916 ^
9.994896
9.994876
9.994857
9.9948 5 1
9.994813
9-
9-
9-
9-
9-
9.
9-
9<
9'
9'
51
52
55
9.1870911^.994798
9*187905
9.188711
54:^189519
55l9-i9'o5i5
9.994779
9.994759
9.994759
9-9947 1^
9-
9-
9*
9-
9-
56
57
58
60
9.191x50
9.1^1955
9.994699
9.994680
59 9-195554
9.191754^.994660
9-99^^40
9-1945 51 19-994610
9-
9.
9-
9-
I9-
74499
75561
76114
77084
7794^
78799
0.8146^8
0.815776
0.8119x6
I0.811057
0.811101
79655
80508
81560
81111
85060
85907
84751
85597
86459
87180
88110
88957
89794
90629
91462
91194
95114
95955
9478(5
95606
96440
97^55
98674
98894
99711
6^15501150
0.810545
Oj8 19491
0.818640
0.817789
0.816940
^9
18
*7
16
.V
14
11
II
10
0.8 1 6091
0.815249
0.814405
0.815561
0.811710
0.811880
0.81 1041
0.8 X 0206
0.809371
Q.808558
18
i6
14I
^5
ii
II
to
0.807706 ^
0.806876 8
o;8o6o47
0.805110
o .'8o4594 i
0.805569
0.801747
0.801916
0801106
6.^00187
4l
3
1
I
d
I Co-fine [ Sine | [Cg>t^«g.| T angent iM
Degree 81.
G 2
liWMMktfMhMU
'
■>^
M
■ . ' ' ' ' I, *
Degree p.
Sine I Ce-fine \ (Tangent | Cfo-tafkr. \
I
z
I
5
5f'i?59i5
9*196718
9.198J02
*9«994^PO
9.994^«o
9.994 566
9-994540
9-994519
9,1065x9
9.XOH45
9*xoii59
>io£97 1
i9.io}78z
7
9
o
9« 19909 1
9.IJ9879
9»ioo66^
■
io.79947oj,59
10.798655
10.797841
10.7970x9
10.796x1.8
9*994499
9*994479
9-994459
9.XOI 451 9.9944 j8
9.10x23 4 19«9944 1 8
9..10459X
9«xo54Qo
9.206x67
10.795408
10.79^600
»o*79379J
9«xo7oi 3 1 10.79x987
9.207817110.79x18 g
1J9.205PX7
2 Si'.x'05^.97
J 9-xo4'577
4 9-.*'05354
5l9-^o6i3i
— •-*
6
9.994398
9-994^77
9.9943 57
9-99'4356
9*994? 16
9.1086x9
9«xo|j^4xp
9*xioxxo
9«xiioi8
9.XvMfti5
9.'xo69o6
7[9*»07679
9.208451
10.79x33^1
*o»79o58o
L0.7 89780
10.788982.
10.7^^8185(45
5«
,56
1!
54
u
Si
U
Jo
4^
4«
47
46
XQ 9.X09991
9*99^^9S
9.994174
9.994*54
9.X09XX2 9*994xJ3
9»99^^^T^
|9.xix6ii
9.X134C5
9.XI4198
9.^4989
9*115780
13
14
15
26
9.x 10760
x{9.'xii526
9*1*1x291
9.SIJQ55
9.i'i3Bi8
9.994191
9-99^171
9.994150
9.9941x9
9.991^108
9.X18142
9^18926
9.x 1 9710
17
28
?o
9*114579
9.fti55?8
P.xi6q97
9.X16854
9.X17609
9.994087
9*994q66
9.994044
9.994024
9.994<K>3
10.787585144
10.786595I4J
X0.78580XI4X
10.7850X1I41
^o^4Xio|4o
39
38
37
5^
35
9.1 16568110.78 34 5 a
9.XI7J56 10.78x644
10.781858
10.781074
10.780x90
9bxxo49i
i9*xxix7X
9.XXXP5X
9.iiiftjo
9.xi56o7
io.7795o8|34
10.7757x8 jg
*o*777948 3x
10.777170 31
ig' 77^3 93(30
J. Co-fwe [ Sine J^^^Co^i^ j Tang ent | M
Decree 80. ~^
ir^
Degieep.
^. Sine I C(hfiM I ITangcntlCfl-*tfa<r. I
io!9^ii76o9 [9.^400 } I I9. 1 X ? 607]
i6
9*£X9ii6
9*%I9864 9*9^39^9
9.221^67
9*99i9^o
t6\
40
9.993918
9*993897
9.2143 8 X
9.22$t55
9.2x59*9
9.226704,
9.2x7471
9^222x15
9»22286l
9.223<So6
9«5993875
9»9938S4
9-^38ja
9.224349 9.9j^38u
9.225o9x|9;99J789
4f
4*
9.225833
9.22^^73
43 9»»i73i»
44 9«*3^8o48
45l9-i»8784
9.*X2824o
9.2 29007
9.229774
9.2JOJ39
9.X3130X
9.9937^8
9*993746
9*993725
9*99J703
9.993681
9*232065
9.2328x6
9.233586
9«i34345
9.X35103
49
9.xx95i8
46
48J 9.x 3,0984
9-13 »7» 5
50I9.232444
51
9-99 3^^ol •
9.23025x19.993638
9*991^ 16
9*991^9^
9.99357 a
9.X35859
9.X366X4
9.237368
9.238120
9*»3887x
51
13
54
55
9*i33i7i
9^33899
9.1346x5
9'»35349
9.993550/
9.9935x8
9.99350^
9-991484
9:^36073 J9.99J46X
9.2396x2
9.3^40371
9,x4iii8
9^i4>865
9.x4x6io
56
57
59
9.13^795
9-1375I5I
9.X38835
9.139670
9.993 #40
9*99341?
9*99119^
9*99iilA
9> 99335
9**43354
9*144097
9*144839
9*145579
9.146319
0.716393J30
0.77 56^J
0.774844
0.774071
0.773300
0.77x519
19
x8
17
26
lif
0.771760^14
13
12
21
XOl
0.770993
0.770x26
0.7^946. 1
0.763698
0.767935
0.767174
0.766414
0.765655
0.764897
'9
18
»7
16
15
0.764141
0.763386
0.76x6 3 X
0.7618^0
0.76 1 IX?
»4l
»3
ix
IX
10
0.760378
0.759629
0.75888X
0.758135
0.757390
9
8
7
6
0.756646
P.755903I 3
0.755 i6i| %
o*7544U
0.753681
i
iCtf^e I Sine | |C(?-^^«g*i Tangent |M
Decree 80,
C3
Ml Sine | Ct^ne \ ITangentj C o-taag, ' (,
Degree
lO,
o\9*^^9^^o\9'9WU\ l9?H^?^^i
4
5
9«ii4iiQi
9«z4l€i4
9,>4x5i6
9'99U07
f.99ji«4
9.993162
9.99J240
9.147057
9.»47794
9.2485 30
9^249*64
9.249998
7
t
o
9-^4?947
9.244656
9.245363
9.246070
9.246775
9.993 1 17
9-W195
9.W5171
9*99 P 49
9.99^17
9.151461
9«i5i49i
9*251920
19.153648
I
2
>4
5
9.147478
9.148181
9.148883
9.149583
9.150181
9-^991 104
9.993011
9.993059
9.99iol€
9.99301^
9.154374
9.155200
9.155^*4
9f 2-56547
9^x^7^^9
1
8
9
20
9*150980
9.151677
9.151373
9.253067
9.253761
9.992990
9.992967
9*99^9A^
9*99 ^9ti
9.992898
9.257990
9.258710
9*^^9^^9
9.260146
9.260863I
21
22
^3
*4
15
9-a'54453
9.155144
9.155834!
9»»565i3
9.i57m
9.991875
9.992852
9.991819
9.991806
9.992783
9.261578
9.262292
9.263005
9.263717
0*164428
26
17
28
19
^o
9.257898
9.258583
9.159168
9*'^^99U
9.260633
9*99^7^9
9.992736
9.992713
9.991690
9.992666
9-i65i38
9.165847
9*166555
9.167261
9.267967
0^5368x160
©•751945J59
o.752ao<>' 58
0-751470 57
0.750756 561
0.75Q002 55
0.749*7€fl54
0*748539 53
0.747^09 51
0.74708^ 5jJ
©•7 463^2^
0*745^2^61
O.744900J48
0.7441 76 J47
0-74345J/46J
0.741731/41
0.7 4 2010 1 44
0*74129045
0.740571 41
Ot739854 41
io .7?^i37 40
0.738422
0.737708
0*736995
0.73628^31^6
0,73557^135
38
0.734862
0.734153
0.733445
0.732739
0.7 3 103 r
34
53
31
31
30
\C<hfin€\ Sine I |C<>-#<y/g. | Tangent |M J
^&^^ 79-
Degree lol
Vf) Sine I Qhfine I ITangenti Co-toHg. \
\o\^.%6o6ii\s^^^z^6\ {9'i^79^7tiQ>7?xoB3l?o
9.%6z6y^
} 519.^64017
$4
9'99»^4J
9.991619
9.991595
9- 99*57*'
9-995^ H9 1
4168671
9t^9l7S
g* 17667 7
$1.170778
9.^71479
W.731J19
J0.7 30615
10.71^913
1:0.71911 X
10.718511
19
18
*7
i5
561^.16470^
37 9'^^U1^
1% 9.ft66o5i
39 9.166713
4019.167395
9*99*5x5
9.991501
999147S
9.991454
9.9914JO
41 9.1^065
41 9.168734
43 9»*^94o*
44 9.170069
45 9-*707?5
9.991406
9.991381
9.992361
9-99*335
99913x1
l6| 9.17 1400
.7 9.171063
9.171716
9.173388
9.174049
9.991187
9.991163
9.99**39
9-99** 14
9.992190
9.174708
9-*753^7
9.176015
9.176681
9-*7733 7
9.991166
9.991141
9.991x18
9.991093
9.991069
9.277991
9.278685
9.179197
9.179948
9.180 J99
9.991045
9.991010
9.99199^
9.99X97JL
9-99^947
I Coi^iif I Sine |
9.171178
9.171876
9.*73573
9.174169
19.1749^4
X 0.7 17 8 11
10.717114
10.716417
X0.715731
X 0.715036
14
*3
12
21
16
9.175658
9^7^351
9.277043
9.*77734
9.178414
10.714341
10.713649
1 0.721957
10.711167
10.711576
9.179113 XO4710887
9.^79^^!
9.181174
9.181858
10.710199
9.180488 ip.7 19511
10.718816
10.7x8141
»9l
18
17
16
15
I4i
13
xil
II
10
9.181541
9.283115
9.183907
9.184588
9.285168
fxo.717458
10.716775
10.716093
10.7x5,412
10.714752
91
8
7
9.18 5946
9.186614
9.287301
9.287977
I9.188651
10.7x4053
X0.7JJ376
X0.7X1699
xaxiioi^
10.7 1 1 348
^p*
C4
1
^ Degree lOy
Ml Sine | Co-fine | iTan gentj C ^tang." I
4
5
9.11411011
9«i4iBj4
9.»4x5i6
9-J^9553'9
9-99^07
9.9952«4
9.>95262
9.995140
9**47o57
9.347794
9.148530
<^.X49a^4
9.149998
7
t
9
10
9.24J947
9.2446^6
9.245363
9.146070
9.246775
9.993 1 17
9-9^3195
9-^95 171
9*991^49
9.99? 1 17
9.251461
19.252491
I9.252920
.253648
II
J4|
J5
9.247478
9.248181
9.248883
9.249583
9.250282
9^993 104
9.99 joii
9'99ioS9
9.991016
9'99lo}i
9*2'54374
9.255200
9.255^24
9f^^6U7
9.257*^9
w i
16 9.25^0980
17 9*151^77
1« 9.252373
199.253067
*o 9«i537^i
9.992990
9.992967
9*99^944
9*99^9^^
9.992898
9.2579901
9.258710
9.259419
9.260146
9.260863
21
22
*3
*4
»5
?'i54453
9.255144
9.99*875
9.992852
9.255834 9.992829
9.256523 9.992806
9.i572.li 9-99*7*3
9.261578
9.262292
9.263005
9.263717
9*264428
26 9.257898
27 9.258583
28 9.259268
29:9.259951
JO 9.260633
9.992759
9.992736
9.992713
9.992690
9.992666
9-*65i38
9.265847
9.266555
9.267261
9.267967
04753681^60
0.75194? I 59
0.751X06^58
0.751470
0.75075^
57
56
0.7 50002. [5 5
0.749*70^154
0.748539 53
0.747809^ 52J
0.747080 51
0.74^3^*^50
0.745616
0.7449<^o
0.74417^
0.743455/4
0.7427 3 »f-
49
48
47
0.742010
0*741290
0.740571
Ot739«54
0.2^9137
44l
43
41
41
40
10.738411
0.737708
0-736995
0.736183
0*73557*
37
35
0.734861
0.734153
0-733445
0.731739
0.73103?
34
33
31
31
30I
\C<h'fin€\ Sine I |C(H»^»g, | Tangent |M
kMDtoMiMita
Ekgrce 79,
-■.r
Degr ee lo*
Mj Sine I Confine I jTangcnti Co-tang. \
— '
5»
S4
M9*^4?
9.99^619
9-99*57*
9'99^^^9
%^9l7S
ga76e77
9.170778
9-»7i479
10.731519
10.75061$
10.71^915
):o,7ipzii
10.713511
19
18
16
i5
3^
37
39
40
9.16470^
9.^65 578
9.ft66o5i
9.166715
9,167595
9.991515
9.991501
999*47*
9.991454
9.991430
9.171178
9.171876
9^*73573
9.174169
9.174964
41
4*
43
44
9.1^065
,9.168734
9.169401
9.170069
45 9-*707 ?J
-t6j9.i7i4oo
47|9.*7*o65
8 9.171716
9.175588
9.174049
9.991406
9.991581
9.991361
9-99*^3^
9991511
9.1756.58
9'^7^35i
9.177045
9.»77734
9.178414
X0.717811
X0.717114
10.716417
10.715731
10.715056
*4|
*3
11
II
16
10.71434*
10.715649
i'o.7ii957
10.71116^
10.711576
^91
18
17
16
t5
I
49
50
9.991187
9'99^^^l
9-99^^19
9.99izi^
9.991190
9^i'79^^3
9.*798di
9.180488
^,181174
9.181858
1 0^710887
10.710199
ip.7i95ii
10.718816
10.718141
XI
II
10
51
5*
53
54
55
9.174708
9.*753^7
9.176015
9.17668 1
9'*77337
9.991166
9.991141
9.991x18
9.991093
9.99106J1I
9.181541(10.7 17458
9.185115
9.185907
9.184588
9.185168
10.716775
1 0.7 1609 5
10.7114x1
10.714751
8
7
56 9'^7799^
57 9.^78685
5« 9*^79^97
59 9«*79948
6o|9.i8oj99
9.991045
9.991010
9.99x996
9.99197^
9.99^947
9.^8 5946
9.186614
9.187301
19.187977
I9.188651
1
10.714055
10.7 1 3576
x 0.7 1 1699
ia7iioi^
10.711548
1
C(N4f«e j Sine | iCo-#^«f. I Tangent IM
Degree 79 '.
C4
ri»
£
Siae I Co-fine^' i Taqgctiti C o-^att^. V
I L " ■* " ■ . ^*' "' * * i ' ■■■■■'■ '» ' -^ ' ^ ^ * . " ' ■' ' #S t > f
Q.7lX348!6o
oi 9.3.805 99I9.99X947 1 1 9^ >^^^^^
■ ■ I. — L ■ 1'^ .. ^ I '
4
9«i8i&a9|9.99i9ii
9.181^97
9.18x544
9.183x90
5 l9*i8j{836
9.99x897
9.99x873
9.99x848
9.991813
9.189316I
9.189999
9.»9©^7J
9.19x34^
9.191013
7
8
9
10
CI
XI
14
15
9.184480
9. 185x^4
9.>'?57f^
9.186408
9,187048
9.99x799
9-99^774
9-9^J^749l
9.9917*4
9.99x699
9.191681
9.19^50
^.194017
9.194684
9.195549
9.187688
9.188316
9.188964
9.1^9600
9 99^^74
9.991649
9,99*^^4
9'99iS99
9.i90i36l9*99»574
9.19604 3
9.196677
9-^^7119
9.198001
9.198661
0.710674
0.7X0001
0-70931,9
o.7o?65|
0.707987
^9
58
51
0.7073^8
0.706650
0.70 59^ J
0.7053x6
0.704651
54
51
51
0.703987
,4^
4«
*47
10.703313
0.70^66 X
070x990
o.70i3?8r4f
^
9.19087.919.99x549
9.19x504
9.191x37
9.191768
9-^91199
1^
17
x8
19
10
II
11
•3
»4
M ^
16 9.197 xq4
17 9 197738
18 9.19S4X1
*9 9.»990?4
SO 9.199655
9.99«5i4
9.991498
9-991475
9.99x448
9''^99l\^
9.199990
9.300638
9.30x194
9.30x951
0.700678^41^
:o.70ooioi4j
0.69936114^
0.698705 4^
0.698 649 140
9.194019
9.194658
9.1^5186
9.1959-1^
9.»9^5J9
9.991411
9^-99^197
9-991 37t.
9.99154^
9.991311
9.301607I
9.3P5161
9.303914
5?4<^4567
9,3051x8
0.697393
0.696739
0.696086
0.6954 J 3
0.694781
39^
3«
37
35
9.9^x195
9.99J'i70
9-99 1144
9.991118
9-99Ma3
93058671
9.306519
9.307168
9307816
9^30^46^
0.6941 3 X 34
0*693481 33
0.691831 31
0.691x84 ^t
o.69X53Zr3o
Pegree 78.
^f3ti£
"•■^
^
Degre e
■•»■
II.
Ml
lo\9'^99^iS\9'99^^9^\ l9»?o^4^ 3'
Sine I Qhfine I [Tangent iCa-ttf/ig.i
IS
J4
55
9»5*>o*95
9-30^ 5 »4
9,^01749
9.9^11^7
9*99^^ 4 1
9.991 II 5
9*3 Oft 1 J 3^ 9«99 X090
9.99 1064
?^1?»BP53^4
J7
40
9.303979
9*$o^S9l
9.305*07
9-305*19
9.991038
9^91011
9*990986
9.990960
9.990934
4»
4»
43
44
9*3o^43o(9«9909o8
9.3Q7041
9.307650
9.308159
jf5l9.3o8867
9.990882
9.990855
9.990819
9.990803
47
48
49
50
9.309474
9.3 10080
9.3x1189
9.311899
9*99077 7
9.990750
9.3 1-668 5 9.9907*4
9.990^97
9*99067 1
519.511495
5»9»3»3«97
$3 9.313^98
54 9-3 » 4*97
i?5 ;9*j 14897
i6
9.990645
9.990^?: 8.
9*99059 1.
9.990565
9.9905 J8
f7
9-3 » 549 5
9*3i^09>
J8 9-3i^^89|9*99P'458,
59 9-3»7*84
609.3x7879
9.9905x1
9'9/90485.
9.99043 X
9*990404
9*3o9M>9l
9*309754
9.JX0399
9.3x1041
9.31x685
9-3i»3»7
9.3x1968
9.3x3608
9-3*4*47
9.3 1488 51
9-Ji55*J
9.3x6x59
9.316795
9-3»743o
9.3x8064
9- J 18697
9.319330
9.3x9961
9.310591
9.31x111
9-31J85I
9.3**479
9.313^06
9-3*3733,
9-3*43581
9.314983
9.315607
9.316131
9.316853
9-3*7475
0. 69x537)^0
0.^90891 19
0.690146 18
0,68960 X 17
0.688958 16
0.6883x5 15 '
0,687673
0.687031
0.686391
0.685753
0.68 5 X X 5
0.684477
0.683841
0,683105
0.681570
0.68x936
0*68x303
0.680670
0.680039
0.679408
0.678778
0.678149
0*677 51 X
0.676894
0.676267
0.675641
*4
*3
11
11
2.0
19
x8
17
16
15
/
14
13
XI
11
xo
9
8
5
0.67 50 I 7
0.674393
C.673769
0.673147
0,671515
3
X
V-
|Ca-^«<| Sine I tC< »w«g. | Tangeiiti
_ Pegtee 78
4
Ml S ine \ Co-ftn'i \ iTangentl Ca-tang. (
1787^19*990404! l9'?*7475|^o«^7^y»-5l^o
Degree 12.
0I9.
I
9*
59.
7
8
9*
9-
21
i»4
»5
9
0I9.
9*
9'
9-
9-
19
7
8
9
9*
9-
9'
9'
9'
9-
9-
9-
19-
9-
26 9*
*7 9-
^8 9.
9.
9-
^9
Jo
1847 J
19066
X965S
lOl^O
10840
9^99o377
9*99^M*
9'99oj»4
9.990197
9.990170
9.3x8091
^3x8711
9-J»9?54
9'?*99n
9»J*o^70
ZI4J0
11019
11607
M194
1^780
9.99oi4»|
9,9^011$
9^990188
9.9901^1
9.990134
9.331187
9*^3 1803
9.3314x8
9-5550J3
9^U^
14366
14950
»5»4
16117
16699
9.990107
9,990079
9.990051
9.990015
9.9^9997
9'l^^^S9
9.35487*
9.?354«»
9.336093
9.33670J
17181
17861
18441
19010
^9^99
9.989970
9.98 9941
9.989915
9.989887
9.989860
9-5373«i
9.337919
9*338517
9-339»3B
9*1197 S9
30176
3075?
3i32'«
31903
3*478
9,989832
.9.989804
9.989777
9.989749
9.989711
9.340344
9-340948
9.341551
9.341155
9«34i757
33051 9*989^95
33^i4
34195
34766
55n7
9.989665
9.989637
9.989609
9.989581
9-34?35*
9-?43958
9*?44558
9-345157
9*345755
0.671905
0.^7 £xS$:
o.67p^4»
0.670047
o*66p43of
5<
551
c.6^8 i 575
0^6^8197151
0.^67 58 &Uij
0.666967I51
0.666354(50
O.665741J49
0.665129141
0*6645 18|47
0*66 3 907 (4
0. 663191(4 5
0*66268 9 14
0*662081
0.661473
0.660867
0.660261
4}
4*
41
I40
0.659656
0.659052
0.658448
0.^57845
o;6 57143
39
3«
3^
35
0.6^6642
0.656042
0.655442
HS654843
10.M4145
34
33
3*
3x
530I
\ Qhfwe \ Sine j |Ca-^^wg. 1 Tangent (M
i^W^M^ II I ■ I *l I " 1 I I I ' ' ' ■ ■■ I —— — —
Degree 77. .
— "^i-^— — I Ml II Mil. ■ ^— ^W^M^W^—
. Degree I2.
Ml Sine | Co-fine I iTang^t) Ctntang \
?0'9>??53?7|9*9^958ii l9'?4S75 5i
34
9.335906
9-33^475
9.337043
^ ., 9-337^*0
55|2_338x76
3^19.33874^1
37 9.339306
3^ 9.339870
39 9.340434
40I9. 1409.96
9.989553
9-9895*5
9.989597
9.9^9469
9.98 9441
9^346353
9.346949
9-347545
9.348x41
1 9.3487 3 5
9.989415
9.989384
9.989356
9989318
9.989199
9.3493*9
9.3499**
9.350514
9.351106
9.351697
41
4*
43
44
45
9.341558
9.34*119
9.34*679
9-343*39
9-343797
9,98 917 X
9-989*43
9.989114
9.989186
9.98*9157
9; J 51187
9-35*876
9.353465
9.354053
9.354640
46
47
48
49
51
5*
53
54
5jf
56
57
58
59
9.344555
9.34491*
9.345469
9.346014
9.346579
9.9B9118
9.989100
9.989071
9.989041
9*989014
9.355**7
9-3558x1
9-356598
9.35698*
9.357566
9.347134
9-347687
9-348*40
9.34879*
9-349343
9.9S8985
9-98^956
9.988917
9.98889^
9.988869I
9.358149
91.358731
51.359313
^.359893
9.360474
9.349893
9.350443
J9i35i540
60I9.J51088 9.988714
9.988840
9.988811
9.988781
9.988754
9.361053
9.36x631
9t362iio
9.36*787
9.363364
o£54*45J3o
0.655647
0.653051
0.651455
0.65x859
o.65X*65
17
16
*5
0.6 5067 X 14
0.650078 13
o.649486[i^
II
101
0.648894
0.648503
0.647715
0.647114
0.646535
0.645947
0.645360
1
I
z8
17
16
15
14
^3
0.644773
0.644187
0.643601I11
0.643018
0.641434
II
10
0.641851
0.641 169
0.640587
0*640107
0.639516
0.658947
0.658568
0.637790
0.657115
0.636636
9
8
7
6
4
3
1
1
[ C(hfine I Sine | \C<htang.\ T angent iM
Degree 77.
tTwM
iTangcnt] C^tang. - 1
_gi5.jiio88'9.9887i4l I9.j6j364
io.6j66j6|6o
1
9-JS»6ji
9,88695
9.J63940
io.6j«o6olS9^
>
9.JSJI8I
9.98866$
9.364^1!
.0.6J5+B5 58
}
9.J5J7»«
9.9386jtf
9.365090
10.634910 57
4
9-J5417"
9.98860V
9.! 6^6.54
I0.6J4H6 S6|
J_
?.JS*'*1
9.9S8J7!
9.?6S,J7
io.6jj76j 5
"
9.J))M8
9.988548
9.3668.0
»0.6jjt9o 54
7
9-JSS90*
9.98«S>9
9.!'S7j8i
io.6ji6iS 53
1
9-JI644J
9.988489
9-ih9n
J0.6J1O47 51
9
9.JJ6984
9.958460
9.J«8J»4
io.6ji476 ji
lo
9.Ji75>4
9^83410
9.369094
10.630906 50
fi
?- 1 58264
9.98840 »
9.369663
10.6JOJJ7 49
i>
9.JI860J
9.?88,7.
9.370»}»
10.619768 48
>i
9.3i9'4i
^988j4i
?. 170799
10.619101 4;
1+
9.1)9679
5.988 J, i
9.J71J67
io.6iS6jj 4<i
is
■9.i!otii
9,988181
9.I7i9iJ
.o.6i!o67 45
t6
9.3607 u
9.988 IS »
S- J 7 1499
10617S01 +4
•7
9-jfiii87
9.988rij
9.J7J064
10.616936
4J
i3
9.i6i8ii
9.988191
9.37J^i?
10,616371
41
»?
9.3fii!iS
9.98816;
9-V^^9i
10.61 5 ?o7
41
9.j6iS89l9.9Bgijj
9.'.747S6
10.615144
40
9.}6j4»»
9.988103
?I7IJI9
10.614681
is
»
j-jfijsu
9.988073
9.J758!>
10.6141 19
}8
»J
9. J 6448 1
9.9880+j
9-576441
io.6ij558
i7
14
9.J6J016
9.988013
9-J77O03
10.611997
3<
It
9.?65i46
9.9S7983
9-37756J
10.6114J7
3J
9,j66o75
9.987953
9.1781"
10.611878
34
17
9.366604
9.987911
9.J786BI
10.611319
a
lE
9.}67iSi
9.987891
9-179H9
.0.61076 <
»9
9,67655
9.987861
9-179797
10.61010J
JO
3..,6Si85
9.9878111
9.!Eoji4
.0.6,9646
L<
1 Co-fat i Sine I ICc
Degree 7'
Degree 13
■»•■
mmb.
M| Sine \ Confine t iTangcntI Co -tang. \
? 0)9*^68 18^19.98 78^1! 19. 380354110.6196461^0
9.368711
9.369136
9.369761
? 519^17080819.987679
5^
5^1
94987^01
9.987771
9.987740
9.987710
19.380910
9.381466
9 381011
9.38a575
9583119
10.619090I;
10.618534
10.617980
10.617415
10.616871
^7
59
9#37i330
9.371851
9.?7iJ7J
9.987649I 1 9.38 368 1
9;9876i8| 19.384134
9-987588
9-987557
9.987 5i6|
9.384786
9.385537
9.385888
10.616318
10.615766
10.615114
10.614663
10.614111
41I9.J739J?
I41 9.J7445*
43 9*374970
44 9»J75487
45l9-?7^oo3
9.987496
9*98^4^5
9^987434
9.987403
9.9S7371
9.386438
9.386987
9*387536
9.388084
9.388631
10.613561
10.613013
ie.611464
10.611916
10.611369
[46 9.37^519
9.J77035
9.377549
9 94378063
Hjd|9.378577
IS
9.987341
9*98^310
9.987*79
9.987148
9,987117
5119/379089 9.987186
^119.379601
53 9I380113
5494380614
55 l9f38ii?4
9.389178
9.389714
9.390170
9.390815
9.391360
9.987155
9.987114
9«98709x
9.987061
I9.391907
9.3914^7
9.392989
9.393531
9.394®74
io.6io8ii
10.610176
10.609730
10.609185
1,0.608640
569.381643
579.381x5*
58 9;38i66x
59 9«38}i68
1 609.3836 75
9.987030
9; 98693 6
9*986904
9.394^x4
9.395154
9.39^133
9.3^771
10.608097
10.607553
10.607011
10.606469
10.605917
10.605386
10.604846
10.604306
10.603767
io;6o3i3?9
5
3
^iCH^e'l Sine | |C g-f4;i g. | Tangen t IM
DegreeTtfT" ~
<-■ ■ ■ I I ■ < »m
3
4
5
Degree 14>
Ml Sine | Cthfine I \T2ingcnt\Co'tang^ . /
019,38367319.98690^1 19.^96771
9.384181
9.384687
9.385191
9.385697
9.386201
9.986873
9.986841
91^986809
9.986778
9*986746
9*197 ^09
9.397846
9.J98383
9.398915^
9. J 994 5 5
0.602694
o.6o2i 54
f 0.601^17
o«'6oi(>di
0.600545
7
8
9
o
9.386704
9.^87*07
9.387709
9.388x10
9.986714
9.986683
9:986651
9.986619
9>38^7" 9.986587
9*$ 99990
9.400514
$^.401058
9.401 591
9^402 124
9*3^9^^^
9.389711
9;390}io
9.390708
9.391206
9.986555
9^986523
9; 98649 1
9i9»6^^9
94986427
9*402656
9.403187
9.403718
9.404149
9.404778
9.391703
9.392199
9*l9^h^
9*191^90
9.393^85
9*986395
9.986363
9.986331
9.986299
9.986266
9*405306
9.405^36
9.406364
9.406892
9.4074^9
*4
»5
9-J94I79
9.394^75
9.395166
9.986234
9*986201
9.9^6169
9.986137
9^6 150! 9.98 6104
9^407945
9440847 J
9^408996
9,409521
9.410045
0*6032x9160
5J
58
5^
55
0.6000x0 54
0.598942 5
0.598409 51I
0.597876 5
o- 5 97 5 44)4!
0.59^813141
0.596282I4;
o.59575i/4<
o,595»ii|4fi
0.594692I44
0.594164 43
o;595^3^ 4^
0.593^08 41
0.592581 4c
0.59*055 39
0.59M19 j8
0.591001437
0.590479
0.589954
3^
31
26 9.396641
*7 9.397131
*8 9.597621
19^.39^111
50
9.398600
9.986072
9*986039
9.986007
9.985974
9.98594^
9.410569
9.411092
9«4zi6i5
9.41x137
9.412658
0*589431
0.58 890S
0.588385
0.587863
0.58734*
34
3*
30
■ >«» ^ -i-. — I ■ ■ « ■■■-. % A
Co-fine I Sine . | \C(^tang. \ Tangent jMl
mmm
Degree 75*
rtm
J
Degree 14.
n
Ml Sine 1 Cthfine | .Tangent | Cortangr. \
go 9.598^oo|9.98$94i| 19.411658 10.587541150
31
p.399087
9.985909
1
9.413179 10.586821
19
?i
^399575
9.985876
9.415699
10.586501
i8
33
9,400061
9.985843
9.414219
10.585781
17
J4
9.400549
9.985811
9.414738
10.585261
16
35
36
9.40io^5
9.985778
9.415157
10.58474^
15
9,401 510 9.985745]
9.415775110.584115
14
37
9.402005
9.985712
9.416295
10.583707
13
38
9.402489
9.985679
9.4x6810
10.583190
11
39
9.402972
9.985646
9.417316
10.581674
IX
40
9.403455
9.985^13]
9.4I7842
IC.582157
2X>
19
41
9.403938
9.985580
9.418357
10.581641
4i
9.404420
9-985547
9.418875
10.581117
-18
43
9.404901
9.985513
9.419387
10.580615
17
44
9.405382
9.985480
9.4 1 990 1
10.580099
16
1
45
461
9.405862
9-98 5447
.
9.42O41 5
10.579585
15
14
9.406514
9-985414
9.420927
10.579071
47
9.406820
9.985580
9.421440
10.578560
13
48
9.407299
9.985547
9.41195 1
10.578048
12
49
9.407776
9.985314
9.422465
10.577537
II
50
9.408254
9.985280
9.411973
10.577016
ro
9
51
9.408731
19*98 5247
9*413484
10.576516
5x
9.409207
9.985215
9.413993
10.576007
8
53
9*409681
9.985180
9.414505
10.575497
7
54
9*410157
9.985146
9.425011
10.574989
6
55
5^
9»^io6i%
9.98511,2
19.415518
10.574480
5
9.411106
9.985079
9.426027 10.573973I
4
57
9*411579
9-985045
'9.41^534
10.^75466
3
58
9.412051
,9.98 50X I
9.427041
io;57i959
2
59
9^41*5^4
9.984977
9.427547 10.57145?
I
60
9.41299^
.9.984945
9.428052 10.571947
1 C(^-i7«e 1 Sine Co-tang | Tai^gent
t
. Degree. 7 5.
J
■ . Degree . i $;
Ml Sine | Confine I iTangent iCo-t^^. i
01 ^41199 6 9,9849i»4l l9.4i8oUl
' " . ... I ■ ■ ,,a ; ^m I '.
1
1
4
5
9.4IJ4^7
9.41395^
9.414408
9.414878
9.415547
9.984910
9.984876
9,984841
9.984808
9.984774
94i8s57|
9.419067
9.4190^
9.4 J 0070
9.4J057i{
6I9.415815
9.41618 J
9.416850
9 9.417**7
10 9.417684
7
8
9.984740
9.984706
9.984^7 i
9.984^^7
9 9«4^o J
IX 9.418 149
II 9.418615
15 9.419079
M 9,4i9U4
1 519*410007
16 9.410470 9-9^4? 97
9.984569
9.984535
9.984500
9.984466
9.984431
X7?.4*09J3
18 "9.41139^
19^411856
1019.411317
9.9^43^3
9.984318
9,984193
9.984159
11
11
13
14
15
9.411778 9.984214
'9 4i3i^"8 9.984189
9-4i3<^97
9414156
9.414615
9.9841,55
9.984110
9.984.085
■>,.
i6] 9.41 5071
9.41 5 5 JO
9.415987
9.41644?
9.416899
17
18
»9
to
9.984050
*9.984oi5
9.983980
9.983945
9.98-^91^0
9.431075
9.431577
9.4J1079
5f.'43i58o
9.433080
9.455580
9.454080
9.434579
9.435078
9.435576
9.436073
9.436570
9.457067
9.437563
9.458059
9.438554
9.439048
9-439543
94400.36
9.400519
9.441011
9.4415x4
9.441906
9441495^
9.441988
0.57 1947 !^o
0.57144a
0.5709?*
0.570454
0.569950
0.5694x7
59
V8
57
5^
55
o.56^9s5J54
0.5684x3 55
0.567921 52
o.'5674io 51
0.566910
0.5^641914
o;565^2o 4
6;56543Ci|4
ziUi
>.5^49'
Q.5644i4f 4
0.563917U
o.r634jo 45
0.561935 42
0.561437 41
0.561941140'
0.561446
0.560952
o.,56o457
0.559964
0.559471
39
38
3^
35
0.558978 54
0.558486 53
o.5579?4 31
0.557503^ f
io.<57oii|3
I Cfh^pne I Sine | iCo^tarijB^.iTapgcnt
^. . . . ., Degree 74.
i»^ M
mm
»5
e I Cei-fiHt \ |Tang ent Ko-tMg. \
IS
55
9.9^^875
9.935840
9.98^770
f9237.?5
I9»44i9^8| loj 5701 1] 50
10.5 5^5 zi[>9
10.55^051 i8
ro.555c?53;i^
9-44? 479
9* 44? 9^^
9.444458
^ 444947
9*4454 ? 5
59
9*43097^
9.985^99
9.9836^4
9.44592.3
9.44^41 1
9.446898
9447? 84
10*554077 jk^
10.553589 >3
10.553l.O;i ii
10.551615^41
9^47870) 1 0. 5 5 ^ 1 2<g
iC
4:r9«43^879J9*983f»?
4*1 9»43 ^3 2^ 9-983487
Wi ^5^778 9.98 J4J»
»4(^4??*ai^P*98j4X^
♦9 9'43 3*74^9-98 3 380
4(71
■ii II 11 .11 ■
9.448356 xo.5 5^^44
9x448841. 10*^5115^
9 4493*^
9*449870
9 450194
9*434 1 » 9.983345
^4145^ 9»983309
MU<^^ P-98ji?3
>4Jf4HP'98ii38
•T
5i
9»4jf|53
<0*9-4!<9i* 9-9*3 »o»
9^983166
5^983130
^ , 1^985094
9jJ|8£afe9|9^83oaji
5^19^4^ 8 5.7^"
10.5^0674.
i(©»55oi.8i
10.54970^
^5
18
*7
5?P^43>>4ft
i5
9*450777
9^5x160
9-45 174 J
9»45>»i5
9j4fi7o6
w>.549ix3
10.548740I1J
^.548*57
io.547775'
JjO. 547*94
i7
f8
9*«9^»4
^•449*97
9?4403.J8
9.982986
9.98»95o
9-^91^^^ |t98i9«4
9<^2<78
9«98aJ$4«
»4«««7
S>.453^^8
^^4148
9-454^*9
9»#55i07
xo«5468i^
^0.54^3^
xo.54li5*
10.54537*
xo.54489^
9^455586
9.456064
9-45^54*
9.4570x9
10.544414
xo.543>3^
10.543458
X0.5 4x980
9*45749^ U^*54*5o3
<m
\C<H^ I Sine \ [ Cthtan ^l I Tangent |M
D
i^MMMf
&
N
De gree \6\
M^ Sine I C(h/?«« I Tamgetitj Co^ar^^. |
I
1
J
4
5
9.440778
9.441118
9.441658
9.441096
9.-4.'^iJ.?^
9.982805
9,^82769
9.982733
9.982696 •
9 982660
9-45^449
9-45«92'5
9.459400
1®^^4^ 55^
loj^4<'<^o^
7
8
^i
10
9-44*975l9-98*^2.3
9:459^75^0.^401*5
- --.^..— _ 1- -
57
5^
f5!
9.443416
9,443848
9.444284
9444/20
9.982587
9.982550
9982514 ,
9.98247711
9.46o349Ht),H<;^ei5i
9.4608 2^1 jbrff^t 77
9.461297
9.461770
9.462242
54
ib.531^250 ii
i^-f?775Sl5t|
<8
it)
ii|9.^4fi55
9.445599
9.446025
5^.44645^
12
14-
9.98244i['
9.^82:164
9.982367
9.982330
9:44689319.9822941
M il l 1 • ■■ 1 . ~ ' ^
16
9:44^ 3 26
jH9-447759
9:448 1*91
9.44^^623
9*449054
9:9^22571
9.982220
9.982183
9.98^146
9.982105^
9:4627 f4U<?:5 5 7:i85}45
9.463 i86|io-^563 14 4i
9.46^658
9.464129
9.464599
liKiJ«^» rfr I ■ •
^o:5:5^t4il47
i>^;555lf'W
yo:f?49?i\44
r<xfJJ^9(x
4^
4^
I
4<
2 2
i9
9.44948^5
9-449$ 15
9«f^[oj45
9^450775
9-45 i 2.03
• •■■ Tl- ■ ■ I 11 —
9.9856^^
9.98 i^M-
9.98 1 9f«
9.9819^1
9-9819^3
i
9:465069
0;465559.
9 466008^
9.46<547.6 , ^ _ ^ .
^.466945! fo.5U<>f 5 4<'
j5
n il I ■ ■■ M^^MiM— — — ^M^.—
9.46t4i^?]^oc5J«587
^678^6^ "
5».468'j4f
^.4688x4
|9.46928<J
io.5§a^tfo
9.451632
27 9 45^d6d
a» 9.45*4^8
^ 9:4f>'^i^5
^of9«45 314^19 9 ^^7371 1 9-47 160 5
9.9819^6
0.98X8^9
^.9818:11
9.98X774
9.4697 46 1 10.? '3 0:254 IK
I9.470211 16.5*978911
•9.47067^!! 0.5 1.95 »4 31
9«47iX4ri|ro.1^S859 %%
V I Cfhfim \ • Sine' li "^o^ang. tTi^geiit'lM
III n il ■ m il I ■■■■ -I.I.III | - . ifcli w m n
Degree i <f .
_^_ : _ J
Ml Sine | Confine \ jTangentl Cort^^ . I:
31
34
35
9-454194
9.454^19
9-45S944
9.4^5469
9.981699
9.981662
9.981624
9.981587
i?,98i«49
9.4,7>o6a
9-472.$3i
9-47 a99 5
9-47 MS 7
9.47J919
36
37
39
40
9.45 5«92-
9.456516
9.456739
9.457162
9457584
9.981512
9.981474
9.981436
9.981398
9.981 3 6j
9.4743^^
9»47,4^42'
9.47530s
9.475763
9>47v^ii3
41
42
43
44
45
9.4T^pa6
9-45842.7
91458848'
9.981323
9.981285
9.98124^
^.459268 9.981209
9,459^84 9981171
9.47'6683
9/477142
9.477601
^.47805^9
9.478517
46 9.460108
47 9-46052^
48 9.4^9946
49 S'^^il^
50I9L.461782
9 9^ 11 1 J^
^.98109^
9.9810.57
51.981019
9980980
9-478975
9-'4794Sl
9.479886
9.480345
9.480801
51
u
54
55
9.46* 19919.930942;
9«,46a64.6 9.980904
946303 2 9.980864
9.46 J 448 9.9808^7
9^46386419.980789
9.481157.
9.48'*iW2
119.481167
5^482^21
9.48 J 07 5
S6
5.7l
59
6o[9.46593f
9.464279
9.464694
9.465108
9,980750
9.9807;;^
9.98067JJ
9.4655Ai[9.98o635
9.980596
9.483528
9.483982
9.484434
9.484887
9485339
0.527931 29
0-^27468 2?
0;5'2'^?S; 27
Pv5.2c6i4?f25
o.siooSi 25
4i
3
0.515619 2
o.li.S-M^ 2
0,524695 22
0-524.237 21
O' 5*37^71 2b
o.?2i3i7 19
0.5 ^1.8 5B 18
0.511399 17
041^^^941 16
0.^1148^ 1.5
o.52ioit
0.5 2® 56.8
0.5*0x11
1 96 5^5;
99
*^^9^,
14
^?
II
0.518743
0.5182815
0.51783^
0.5x7379
0.516915
n
8
'7
6
'5
0.516471
0.5x6018
0.515565
0.515113
.0.514661
4
3
z
I
I Co-Jinf I Sine I \Certang. \tm\%Qnt\M
t
Dearee 72.
■^ — h
«
Ml Smc I Co>^;ie T |;Tangent| Co^sng. \
I
%
9.46676 1
IJ9.467173
#; $.467:585
9.980558
9.9S0519
9.980480
9.980441
9. 98040 g
9.485791
9,48 6 141
9.48669;
10.5141091^
10.513758
»o.5i3jo7
9-4?7i43Uo. 5-1 2857
48759jUo-iii407
f9*
' 8
9.468407 9.9803^64
9.468817 9.98x:>p 5
9.4691x7 9.98018^61
9.469637 9.980147;
9.980108
9.48804.3
9.488493
9.488941
9.48 93 90;
9.489838.
10.511957
10.511,507
10.511)059
X0.510610
io,5ioi6i
11
14
9.470455
9.471863
9.47 107 X
9.471678^
9^471086
9.980169^
9*980 1 3 c|
9.9800911
9.98005 3t
9.980012
9.49018^
9*4907 53;
9*49 1 i8p
9.49i6i7(
9*49 107 3
16
^9
to
$.47149219.979973
9*471898
9*4735^4
9'47 37310
9.474115
9.979934
9.979894
9.9798^5
9.979816
1 1
21
21
2^
9*49*^19
9.49*9^4
9-493410
9-493^14
9.494199
io«5o97^4{i
io.5<j9i67^
lo* 5 088 10^
10.508J73 4
llO-507Q28(4
-* >■ III ■
10*507 4SI]
lo* 50703 5
10.5065^0
10.506 x<45
ro,5o57t}i
9-4745 15(
9*4749*3
9k7il^7
^4 ^47 57301
•0 9-41^^33
9.979776
9-979737}
9*979^9i
9-979^9
9.979618
9-494743
9.495186
19.495^30
9.496073
f-49^515
16^^476536
77^ 9-47^93^ 9*97 9if9
18
30
10.505257
it>.5o4Si3
*o« 504570
io«5o59i8
ip.5034^5
9»47734o
9*477741
9.478141
9.97957^'
9.979499
9*979^^9
9.979419
9.496957
.9-497399
^497840
9.498182
9.498721
I C<>^«e I Sine
10*50304?
io*5b%6oi
10.5 pi 1-60
to.5o«7i8
10^01x78
■^MMMMI
kMM.
D(
|_| C(Mtfi^. I T angent
fee 72.^
Mil
. Degree 17.
Ml Sine I Co-fine I |Taiigent| Co-^ng \
V
21
9.47«Ui
9.478941
9*479342
9-479741
9.979380
9.979M0
9.979^00
9.9791^0
9^480140(9.979110
9.49916 J
9.4996dx
9.^00642
9.500481
9*500920
5^
?7
38
?9
40
9.4805^8
9.48 09 3 6
9.481334
9.48 17 3 1
9.481 1 &!}
9.979180
9.97P140
9^979099
9*979059
9.979019
41
4i
if?
44
45
9.482.515
9*48 191 1
9.483316
9.483711
9.484K36
9*501359
9.501797
9.502x34
9.50^^671
9.503109
9.978980
9.978939
9.978898
9.978858
9.978817
9.50354^
9.503982
9.504418
9.504854
9.505189
46
47
48
49
50I9.486075
9.484^01
9.484895
9.485289
9.485682
19*
9.978777
9.978736
9.97^6^
9.978655
9.97^61^
9/505714
9.506158
9.506593
9.5^07016
9.507459
^119.486467
5*
f4
5$
9.486859
9aH^V
9,487642
9.488033
9-97«574
9-978 53 J
9.978493
9;978452
9..978411
56
f7
58
59
60
9.488414
9.^8814
9.489204
9-489193
9^48^82
9.507891
9.508326
9.508759
9.509181
9^509622
9.9^8370
9.978329
9*978288
9.978247
9.978206
9.510044
9.510486
9.5x0916
9«5ii34^
9.51177^
0.500837
0.500398
0.499958
0.499519
0.499080
»8
29
\^7
16
0.498641 14
0.498103 2 1
0.497765 22
0.497318 ij
0.496891 ip
0.4964 54
0.496018
0.495582
0.49514^
0.4947 1 1
19
x8
If
16
15
0.4942x6
0.493841
0.493407
0.492973
0.492540
14
i|
J2
II
10
{
0.492107
0.491^74
0*49 1 »4M f
o.49o809J 6
9* 4903771 f
10.489946 4
0.489515 3
0.489084 %
0.488654 i
0.488225 o
C<hfine\ SixK I |:C(?^^ng/| Tangent |M
^«M»l
■ P^"^ 7''
«ki
Degree i8V
Ml Sine •] Co-fine I lTangent| O-j^jilj. |
9^8.998219.978106119.5x1776110.483^14,11
'
z
4
5
•9;4?oj7i
9.490759
9.97 8 c6 5
9,9781x4
9.491147 9.97^0$ J
9 49i9i2]9. 978000 1
9*5 xztLo6l 10*487794
9.J 1 2.65 51^0*487^65
9,515064
9*5 M49?
9.5i?9ii
io.'48 55o7
10.486079
9^492-^08
7 9*49^^95
8 9.495080
9.495466
io'9«49585i
9-977959
9'9779>8
9.977877
9*977SM
9-5 14549
9*5 14777
9.515204
9.515651
10.485^51!
10.48 5a>^
10.48479)5
10.4845^9
9.977794! |9*5i6o57 10*^^^941
5!
5i
5«
II
II
14
X5
9.4941 ?6
9.494620
9.^95005
9.4955»8
9.49J771
9.97775 a
9-9777 1 1
9.9776^9
9.977618
9.97758.6
9.516484
9.516910
9''yi7n5
9.5177^1
9.518185
16
17
l8
19
20
9.496154
9-977544
9.518610
9.496557
9-977505
9-5x9054
9.^9691^
9.977461
9.519458
9.497501
9.977419
9.519882
9.497682
9*977577
9.510505
10.48351614;
10.485090 4!
10*481665 41
io.48ii^9f4J
ic*48i8i4(4
10.48 1 59014
10.480966141
io.48o$4il4:
10.48011814
ic«479695'4
21 9.498065
2 ij 9.498 444
2-4|9-^499*<>4
15
9.498814
9-977535
9-977195
9-97'7i1'
9.977209
9/499584I9.977167
9.5107x81x0.479172
9.511151
9.511575
9-52x995
9.522417
10.478849
1 0.47 S 4 17
10.478005
io.47>585i
26
27
2C
?o
9.499965
9.500^41
9.5ob7io
9.5bio99
9.561476
9.977x^5
9.977085
9.977041
9,97^999
9.976956
9.5118 5^Uo.477 162
9.52^259
9.525^79
9.514109
9.524520
3
10.476741
ro«4765so j
19-475900]
io.4«7548ot:
|- Cg?/?/ze I Sine I | Co-tang \ T angent t'
Degree 1i. ^
D^cc 1 8.
VI I .Sine t Confine V Tangent | Co-^^w^.
5o|9.50J47^ 9*97^9561 !9.Ti45ao|io.47548oho
■■I I- . I ■III II i « . .1 I. Ml ■ I I I- ..m- « ■■ . ■ ' * ■■ » ■■
J I 9«56i8|4^9.97^9i4l
J5
9,502607
9.503984
9^503^6c
9U97^87i
9.976850 ;
9.976787.
^.97^745
9*SM939
9-1^Sl^9
9-5*577^
9.516197
9.516615
10.475060
10.474641
19.474x11
Io.47?So3
io.47??85
1^
37
9.5057^5. 9.976701
o»5o4iio
9- IP448 5
J9J9t50484o
40)9.505x54
9,976660
9,976617
?-97^l74
^.976552,
9*53'705J
952.7451
{^,5x7868
9.5x8x85
9,5x870x
4i
4i
44
45
9.'5o5^o8|9,9764C9
9.5059^1
9*5q^M4
9.5067x7
^.976446
9.976404
9.976561
9.5o709i9!| 9.9765 18
9,5x9118
9-5*95M
9*559950
^.550566
9-5?078i
10,47x967
10,47x549
10.47X15X
10,471715
10.47IX9JJ
10^47088 J
10.470465
10.470049
10,469634
10.469x19
461
47
48
49
50
9.50747J
9*507843
9,5^08214
9-5o?f85
9*5^^955
9.976275 j9-53M9^
9*97^H^ 9f5Ji6ii
^.97^185 9.5310x5
9t97^i4^ 9-531436
9.97^ioj 19,532^^51
^9
18
17
16
x5
10,468804114
10,468589 15
X 0.467 97 5 IX
10.467561 XI
10.467 J 47, 10
5it
51
53
54
52
56
57
58
59
9.5093x619,9760601
9^50969619.976017
9.510065
9.5x0434
9.510805
9.975973
9975930I
9.975887
9.1 3? 1^6
9.533^79
9.534091
9-534504
10,466754
10.4665x1
10.4^5908
ip.465496
9 554916I.10.465084
9
8
7
6
5
9»5lii7i
9-5i;540
9.511997
9.5x1175
6019.51X64X
9.975544
9.975800
9-9757^7
9'9757i3
.9.5 3^318110.464671
-p*
9.535739
9.53^150
9.556561
9'9737»3 y.^5*'>"A
9. 975^701 19-53^971
10^464x61
10.465849
10.465459
10.4650^x8
4
3
1
I
o
i Co^fin$ I Sine I |C^-ttf^l Tangent iM
Degree 71
D 4
m^mt^m
wuuuu^tmaimiti
IMfi
Degtee ip<
[ M] Sine | (>fot e | iTangcntl C <h»^w^> |
I
4
9.5 1 J o©^
Mn375
9.n374r
^.514107
^.514471
to
^5i48j7
9.5152OZ
9.515566
y|9^fM9}o
1
S
9975^1^
9.9755«S
9-97555^
9.97549^
>9'97 545i>
9.975408'
9-9753^4
9-9753**
9975*77
9-97 5^? 5
15
9.516617
9.517010
9.517381
fi49.5i7745
9.518107
9975189
9-975145
9.97 5 loi
9975057
9.9750*^
16
»7
18
19
9.51846S
9.518819
9.519^5^0
9.519551
1019.515^^11
9.974969
^9749*51
9.974880
9.974836
9.97479*1
II
11
13
*4
*5
9.51017^9.974747
9.5*o6ji
9.510990
9.511349
9.511707
9-974703
9.974659
9.974614
9.974570
1619.511065
17 9.51141J
18 9.511781
*9 9*513138
f?o 9.513495
9-974515
9.974480
9.97445^
9.974391
9.974346
9* 51779*^ 10,461 xo5
9.538*02 10.4^1798
^.5386x0 10.4^1389
M^9oi>c 10.460980
5j
51
5<
ff 5 394*9
M39837
9» 540145
9.540653
ie.4CF057j|5^
10.460163
10.459755
Io,4S9347
51
9 .y4io6i|io,4s8939|5fl
10.4585^1145
Io»458ii54l
9.541468
9-541875
9.541181
9-543094
10.4577194?
9.541688 10.457^11/4^
{0.456906(4$
9-543499
9-543905
9-5443*0
9- 5447 M
9*545x19
10.456501U4
10,456095 45
10.455^90 41
10.455x85 4>
IO.454881I40
9.5455*4
95459*7
9-5463 3 »
9.546735
9.547^38
X 0.4 5447 6
10.4540x1
10.453669
10.453265
lo.45&86t
3>
J«
37
3^
35
9.547540
9-547943
9.548345
9-548747
19-549x49
10.45 »459j34
10.41*057 3 J
19.45x655
10.451x53
10.450851
[Co-fine I Sine I 'CM< t/fg> J Tang ent »|1V
Degree yo.
MM*
^•P
Mil
iDegree
19.
mm
mmtrnttk
Ml Sine {Cthfim I ITangeiu:^ Co>fttiig. }
I ■ *^ —
n 9*5*45^4
U|9-5i49»«
57
9*9745 01
9*974*57
9^74* U
9.974x67!
9.9741x11
9^54^550
9*f4995x
d.5
9.5
9^
9.5a56?ol9.974077
9*5x59^4 9^97405*
9*5i^??9 9.9739*7
J9|9-^*66i?? 9»97394i
4019.51704^ 19.973^97
9-f
9.S
9.5
9-5
4»
41
43
44
45
9.5»74O0!9»973S52
9»5»775B
9^518105
9,518458
9.518810
9.973807
9.97 J 761
9.973716
9.975671
46 9.519x61
47 9.519513
48}9.5i9864
49 9.530XX4
i^Ma««*iMM
9,975615
9.973580
9-973535
9-973489!
9.5
9.5
9-5
9*5
9.5
5x
5*
53
54
55
9.530911
9-5 J X 265
9.5J1614
9.531963
9.973 3 9»
9-973? 52
9-97? 307
9.97316.1
9.97UX5
9*5
9.5
9*5
9.5
9*5
56 9.531661
57 9*5330«>9
58 9*53?357
599.5.3J704
6ob^5|4D5i
9.973169
9w97JX23
9-973078
9.973051
9-9 7*986
9-5
9.5
io.45o45«
io.45eo49
0} 5 1 ^0.44964$
0751 xo.44^i4t
1x51 1 0,441^48
1551 10.448449
1951 10*448048
1J5I 10.447649
17I0 10.44^150
3X49PO-44685I
^9
i8
»7
t6
£5
*4
*3
111
%i
s<4
3548
3946
4344
474 X
X 0.44645 2
10.446054
10.445656
X 0.4452 59
^1A9 < 0-444861
18
17
16
5536
5931 10.444068
6319
6715
7lii
75x7
79x2
8508
870!
9097
10.444464
949 X
9885
10,443671
10.443*75
10.44*879
10,4414^3
10.442088
XO.44J693
10.44x198
10.440901
<4l
til
It
xo
t C(hfmt I Sine |
9.560179
9.560673
9.561066
xo.44of<;>9
10.4401 If
io.4J*7*«
io.4?9l»7
x o^f»934
iMl
Degree 7 o>
angcot i«f
• Degree 2 oV
^l Sine I Confine ] Tangcntf Ccntang. \
0,9.5 Ho5i'9.972'986| '9.561-661.1 0.438 9^ 4|6<
X
1
4
5
9.53474f^
9M^9^
9MU17
9-97 »940
9.971894.
9.972.848
p.97z8oi
9.97:17.55
9-5^M59
9.56x851
9.561144
9.$65<7a8
10.43854?
X 0.418 148
10.45775^
10.4575^^
IQ.4?^97*
7
8
9
9.S36xi^J9-97«'709
9*556474 9-971663
9.536818
9.597163
9-537507
9.971617
9.97^570
9.971514
9.563419
9.5638U
9.564101
9.56459*'
1 9.56498 3
10.44(6580
5
10.4^6^89
10.435798
10.435407
xo.45501.7
51
51
501
u
9.537851
9*97^^77
9-56537^
11
9.53?i94
9.971431
9-565763
«5
9.538537
997H^^
9.566153
14
9.538880
9-97^11^
9.566542
15
9.539»*i
9.971191
9.5669U
10.4346*7 41
10.434157 48
10.433847 47
10.433457 46
10.433068/45
16
»7
19
10
9.539565
9.539907
9.540149
9.540590
9.540931
9.971145
9.971198
9-9711 5 X
9.97H05
9.971058
9.567310
9.567709
9.568097
9.568486
9.569873
10.43 167 9\ 44]
10.43 1Z91I4J
10.431901I41
10.43.15 1 4Ux
10.43x1*^140
Ux
11
13
«4
15
9.541171
9.541611
9.541953
9.541191
9.541631
9,971011
9.971964
9.^71917
9-971870
9.971813
9 569161110.430739
9.569648
9.560035
^•560411
9.560809
10.4J0351
10.4299^4
10.419578
10.419191
39
38
36
35
16^9.541971
9-5433x0
9*543649
9.543987
u^
19
30I9.544315
9.971776
9971719
9.971681
9.971635
9.971588
l9.57ii95Jio.4i83o5i34
9.571581
9.571967
9-571351
9-571738
10.418419
10.418033
10.417 648
X 0.417162
33
32
31
3<^
I Cfhfme I Sine | | Co^tang. \ Tangent iM
Degree tfp^
Degree 20.
Ml
• Sine '
Co-fine \ iTangeni
^9.971 588! 9*57173^
— ..... -"jjiji - -:—
l\C(htAng.\
50 9.544?iS
10.4272611
30
^M
9.544665
9.971540
9v57?ii5
X 0.416877
1^
t^^
9.545000
9.971493
9-57?5o7
10.416491
18
^^
9-5453^8
9.971446
9.573892
10*426108
17
24
9-545674
9.97x398
9.574176
10.415714
16
?5
15^
9 54<?oii
9.971 3 51
9.574660110.425^0
15
9.546J47
9-971303
9.575044
io»4i4956 14
• 57
9.546683
9.971156
9*5754x7
to.414573 ?3
3«
9 547019
9.971108
9.575810
io»4i4s89
hil
'
39
9- 547? 54
9.971161
9576193
10.513807
11
t
40 9.547689
9.971111
9.576576
io-4i34i4!2C)i
%
^
Ux
9.548024
9.971065
9.576958} 10.41 3041
T9
42-
9.548358
9.971018
9'57734i
10.411659
18
4?
9.54869;?
9.970970
9-577713
10.411177
17
44
9.549016
9.970911
9.578104
10.411896
16
45
9-549?6o
9.970874
9.578486
10.41X514
11
14
46
9.549693
9.970816, 1
9.578867
10.411133
47
9.550016
9-970779
-
9.579148
1,0.4107 5 2
13
■
48
9-550359
9.970731
9:579618
10.420571
12
49
9.550^91
9.970683
9.580009
10.419991
11
50
9.551014
9.970654
9.580389
10.419611
10
•
51
9-55l?55
9.970586
9- 5807^9
10.419131
9
5i
9.551687
9-970138
9.581149
10.418851
8
»
5?
9.55ioi8
9.970490
9.581528
10.418471
7
%
54
9-55t?49
9.970442
9.581907
10.418092
6
55
9.551680
9.970394
9.53^l86
10.4177'^
5
■
56
9.553010
9.970345
9.581665
10.417^5
4
57
9-55? MO
9.970197
9*5^3043
10.4x6956
15
58
9.553670
9.970149
9.583411
10.4x6573
I
^9
9.554000
9«97oioo
9.583900
10.4x6100
I
Uo
9-5543*9
9.970151I
9.584177
10.415B1J
%
Co'fne Sine
1 iCo'tang. , Tangent 1 M
Degi
ree
6f.
1
\
1
II- - ■' .1
D^SIT
Ml Siie I fiygpii e I ITangcntI Cth-tangm I
58
57
56
55
I X
1
9.^54^58
9-f<4987
J ^.555315
4H55<^4?
5 9«55597^
9.97010$
9.970055
9.970006
9*^^9957
9*969909
9-5S4555
9-58495*
9.585^08
9.585686
9.^86061
T
8
9
o
9»556>99
9.556616
f-55^95?
9-557*79
9.969860
9.9698 1 1
9-969762.
9.9697 1 5
9.96966^
9.5864J9
9.586815
9.587190
9.587566
9.587941
o-4»5445
0*41 5o6^S
0.414691
0.4143x4
0.41 ? 93^
0.4135^1 54
0.4x3185 53
o«4ii8oo 5&
0.4x1434 51
0.41^059150
1
II
3
4
9»5579?i
9«558258
9.558583
9*558909
9*559»?4
9.969616
9.969167
9.969518
9-9^94^9
9.969419
9.588516
9.588691
9*589066
9.589440
9.5898x4
o«4Xi684 49
0.4x1309 4?
0.410934 47
0*410560 46
0/4x0185145
:
7
8
9
xo
9»5595-53!9.96937o
9.55988}
9.560207
9.560531
9.560855
9.969321
9.969272
9.969x23
9.969 1 7 jj
.590188
9.590561
9.5909 J 5
9.59x508
9.59168X
0.4098 1^|44|
0U09438 43
0I409065 42
0.498691 41
0.498319 40
2iJ9«56iX78
22 9.561501
»3 9.561824
24' 9.562146
Miy. 562468
9*9^9x24
9.96907 5
9.969025
9.968976
9.968926
9-59»o54|
9.59H»^
9.592798
9.593170
9-595 541
0.407946139
0-407574 38
Ow).07XOX
o»4o6tfx9
0.406457
26 9.562790
27 9.563112
*8 9*563433
»9 9«5^J754
30 9-564075
9.968877
9.968827
9.968777
9.9^8728
9.968678
9-595914
9*594i85
9.594^5^
9.595017
9>595397
0.406086
0.4057x5
<^-405344
0.405073 ,.
0.404601)30
?7
34j
5*
131
iCi^-jwe I Sine | Co-tanfi^. \ Tangent IM
JOegrec 6%,
''mm
"Dcj^c
21.
Ml Sine \C(hfine \ lTangcnt| Ce-ftwi^. |
\
JO |4ft6407 5 19.^68^78 1 19.595^97' 10. ;o46o.2 i-©
- ^ , f ■ » - ' "' ■ ' I I II III zi^
31
34
^5
5619.5659^519.9^837^1-
3719.566^14 9.9683*8
9.5^439^19.9^86x81
9.564716
9.56505^
9.56535-^
9565675
9.968578
^,968518
9.968478
9.968428
9.5957^8110.404x31
^.596158
9.596508
9.596878
^.597H7
10.4017 J3
2,9
2-7
38
39
40
9.566631
9.566^51
9.567x69
9.968178
9 968 ia8
9.968 178
9.5^8354
9.5987x1
9-^99091
io*4o386(:fc
10.40349a
10.403 sia*| 16
»^
»3
2ii
9.5976161 io.40i3'^4
9.597985I10.40XO15
10.461646
10.401x77'
10.400909)^0
4»
41
43
44
45
9.567-587
9.567504
9.9681x8
9.968078
95^8539
9.568855
9.568x11 9.9680x7
9.9^7977
9.9679x7
9.599459
9.5998^7
9.600x94
9.60056 X
5.600919
1 0.40054 <
10.400173
io.3998t>6
10.399438
10.3.99071
46
47*
48
49
5q
9.56917X, 1^.967876
9.5694B8 9.9678x6
9.569*04 9.967775
9.570110 9.9677x5
>.57«43 519-9^7^41
9.60 j! 196'
9.601 66 X
9.601019
9.601395
9.601761
10.39^704
10.398337:
10.397971
10.397665
ioj97xi^{jb
^9
18
IT.
16
11
11
549.571^95
51
51
53
9«57075i
9.571065
9.57i'3^0
9.9676x311 il9.6o3ii7
9-967573
9.967 5xx
9.967471
5 5 19. 57*00949-967410
9.603493
9.603853
9.604113
9.604588
10.396873119
i<3«3 96507 1 8
ro.396T4i 7
ro.39577? '6
i!o.3954ii.. 5
56|9^57x3ii(
57 9- 57*^ J^
58 9*57*949
59 9-57 3*1^1
^o 9.57? 57 5
9.967370
9-967 r»9
9.9672:68
9.967^x7
9^7x661
9*604953
9.605 3^7
9.605681
9«6q6o46
^606409
Xo.395b47 4
10.394683 .3
10.394*^18
X0.593954
10.393^^9^ o
11
1
\C^Jifie I Sine | !Co-/i«!^g. . Tangent IM
... Dcgee £&^ . . . '
Degree 22.
Ml Sine | Co-fme \ |Tang cnt! Co>^^/zg> t J
.1 9.^73^83 C.967115 9.606773 xo.39j2.z7 59
4
.5
9'
9'
9-
,9^
.i6
!7-
10
9'
9-
9*
9«
M
9-
9*
a6
17
iS
i;9
9-
9^
9*
^Q 9
*««•
11 9*
a 9:
:»^l9.
i7
19
30
IP*
9-
9.
9.
9.
74100 9.967064
74511 9_.9670ii
74814 ^^66^6%
7 5t?5 9>9^^9. i<»
.9.607136
9.607 5 op
9.607861
9.60811^
7 5447l9*9^^3^9
75753 9.966802
76068 9.96^756
76379 9.966705
7h99
77309
77618
779^7
781^6
c),9666oz
9.9^6siO
9.966499
9^966447
9.966395]
9.6o?588
9.608950
9.609311
9.609674
9.600036
10.391.863 I58
10.391500 57
10.391137 5^
10.391774 SJ
14
10.39141 X
10.391050
10.390683
io.3903x^
U
1
10^89964150
9.610397
9.610758
9.6 1 1 1 1 9
9.61 1480
9.611841I
10.3896,03
X0.389141
1.0.388880
10^388510
10.388159
49
48
47
46
45
78545
7885?
79161
79469
7977^
9.966191
9.96 d> 140
9.96^x8^
I i«ii H * ■■ - '
9.611191
9.611561
0,611911
9.61 3641
10.3S7799
10.387438
I0.387P78
91613^81 10.386719
8008419.966084
80391 9.96^0
806.98
8ioq5
.8131,1
iQ.386 j^59
2.96598^0'
9,96,5918
,9.9^5876
81618
81913
81119
81534
9,965814
9.965771
9*9^572'0
9.9656'68
9.614000
9«^H359. , . .
9.6147 18 10.385181
9^.61 5p77po.5 ^4913
! 9'P^U li
44
45
4^
41
40
1.0.386006 [3 9
10.385641138
57
36
10.384565 35
81840J9.965615
9.615793(10.334107
9.6i6^5i\xciy383;848
9^^.16509
.9^616867
I9.617114
i'o-38349i
»o»333iH .
I9j.8277;i6 30
34
33
3*
31
\ Co-fne \ . Sine . | . \C(Hang. \ ^i^ngcnt I
^^^^^7>
Degree 22 1
*«ap
Mi 'Sine' ^ Cthjine < • jTangentI Co-f ^«j^. | ?
jxl>.583i44
35
9.;5«4o5«
9.965563
1^9^'55xi
9p9^5458
9. ^'6 540^
^5
59
9i$>84;6i ;^.^>65^5 ^
»^.9655oi
$1 9^5148
^.965195
^9 55*145
^< 9^6 5 090
9.617938
9.6i8i9f
9w6i«554
9.619008
9.5849f6»
9^58 5^7'*
9:f« 5 <74
5^09,58587^
9.619364
9.619710
9.610076
9.62^0431
^.616787
4i
43
44
'48
49
150J
9.58^i79f9.96.5o37
9.f86if8l
9.^57085
2?r*>386
9*964984
^964931
9.964878
19 964845
9.621 14a
9.^21497
9:62X'8'5i
9.6£i2o6
^.624561
'9;587<*^7
9.587^8^
9; 5 8 81 89
^;588{89
9*5^8190
9,964772
^^9647 1 9
9.^6466*6
9.964613
9^6456
^.622915
9>2f269
9.dl2}62 3
9.623976
.9,624330
511
5i
53
5^
f5
^,5^94»9
'9-5«97V
2^12^^1
9.964^07
f»9^4454
^.964406
9. 59«»*»8' ^9^4347
9,964294
9.624683
9.625636
^^15388
9.625741
9.626093
56
57.
6^
9.^90^86^ 91964240
9*590^8:*
9.591282
^.59«f8o
9.59 1878
9U964I87
9.964133
9.964080
9-9^40 1^
9.6264451
^.626797
9i^i7U9
^j6i75oi.
^•6'27g5i
0.38177^150
0.^8241$^
0.^84061
0.38^705
0.381548
0.38^0991125
*9
48
57
i6|
0.380655
0.380279
0-3799*4
0.37956^
0.379213
0.578858
0.378^03
0;378i48i
0.377793
0.37^439
0.377085
0.37^^ 5<j
o;576577
0.576024
^•375^7J2'
»4l
^?
42
17
16
M
It
i<S
ti
0.3753^7
0.3749^
0.3746^2 'f
0.374*59 ^
o.3739«^r1
o.37j5f5
0.375 ic$5
0.5728^
0.372499
o.3'7Tti48
3
i
I
o
■ »-, 11 "t:.i,
f' Co*^/iet I Sine | [Co^tahg. \ Tangdnt I M
D^ee^?'
Mii-mmm^^
tf| Sine )C^^^ 1 \TinsCat\ Go-tang. 1
o^fity8l9.3g4a>g| ly^t? 8 ji|jo.i7tt48|go
9.5*1770
0-S7IOSS
o.J?0744
oJ7yj+
9-5SJ659
M94»5i
». 594547
9.T94841
3.^6} 7« J
9.965 &5,
9i9^!i9^
9t9*?54a
9 9*!4«8
'*
S.59\>37
».i954i:
_ *i.9i7i7
n5t9.>Ip*6\o
»7| 9.»^:?oj
jB 9.597156
>« 9 »9749o
S-l 98071 U
9f*8i«
?.JS»9Si
?.599»44
19 jr.£0e4a9
}tf 19.6007 ao
9.^t^56
9.6}c^o6
9.6jo6ii
9.63100;
9.S3IJ54
Jo.J?oa44
J 0.3 69694
'o.J^9M4
10468995
TO. J 6864,
9-9^iV9
9.9*JJi5
9.9Sj»71'
9,96^,10}
9.96 J M&
9.9*Jol4
9.96x999
Mli?4*
>96x8^r
9.96*816
^9**7l*
^.9617 16
9.g6t67 ?.
9.6,3 1704
9.^J»MJ
J.6J140I
9.6ji7(o
ip;3*7>47
(0.3675.38
»o. i6<99 j|
9.fi;?447
p.^J*499
p.6j43j.8
, ,961,617
9.p6bj6»
9.9^*S<V
9-9***J^
19.6^5185
S.6jJijj?
k,6jl«79
)9.6]6>a6 I
J9-^J^59>
|9.6j<i9i8
k.6579i6
i9-^i8lo;t
io.36t« S7I
*o.t6ft6
W^J^44^
to.j44ij^
i.o.jtfj77^
«^.?£i4>r
K'.}*»7IS
1 ciHpHf J aj^ ,| iciHiiB^.n^u^ftitB
Ml Sine
begree 23T
^«.=^
[C o-fine] ITangentl C o-^tfffg. I
jo|9.6oo7QoJ9,y6x^98 ) |p.6;8?o2|
35
^6009^0
9.6of^7C
9.6018^0
9.601149
9f9^i»JS
9i96*i78
9.961111
3^
37
39
40
4»
41
43
44
45
9.601459
^.601718
9.603 0I7
9.605305
9-^P?594
9.638647
94638991
9^^3P337
J' 639681
6460^7
9*9620^
9i96ioi2i
9.961957
9.961 901
9.961846
}
9;64037i
9;64o7i6
9*641060
9,641404
9.641747
9.603881
9.604170
9.604457
9.604745
9.605032
9.961791
9.961735
9.961680
9I961614
9.961569
46
47
48
49
50
9^641091
9.641434
Si.64i77»^
^.643110
^^4M^3
9.605319
9.60 5 606
9.605891
9.606 1 79
9.606465
9.6067.50
9.607039
5^.6073 21
9.
51
51
U
54
55'9.6o789l
9.961 51 3
9.961458
9.961401
9.961346
9.961290
S(/9^12'35
9.961179
9.961113
J.961067
9.961^11
9.643806
9.64414$
^.644490
9-^44? 3 a
9.645174
56
57
58
59
9.645516
9.645857
^.646199
9^646^40
9646881
9.60817619.960955
J.6oS^4i5i
9.608745
^.609019
9.960899
9.960842
9.960786
9#647i2i
9.647562
9'^479*3 b^
9.64814^3'
9.648 58 3 1
0.361698130
0.361353
0.361007
0.360661
0.360318
0*3.5997 ?
17
26
i5
P.3 59^*9
O.J 59184
0.358940
0.358596
0.358253
22
11
20
0.357909 19
W. 3 57566 ig
o.3 57^r3
0.3,56980
0.356537
17
16
15
0.356194
0.355852
0.355510
0.3 ff 168
0.3^55.8 26
II
10
03
0.354i4»
o.3fj8oi
0.3534^0
MILL!?
07751778
0^352438
o.\jJio97
S3 J 17 57
?«Mi4?7
9
8
7
6
5
60 9.60 9^^1 j{ 9.9607^6
I CjHJ/^e I Sine J iC(>-f^/?g; j Tangent!
4
2
I
Degree tf 6.
¥
Dec ree 24, "
Ml Sine | define j iTangcnt] Co-tahg \
o\ 9.609^ t^, 9.960730] 19.648 5^11
ij9.6©9597l9.96o674l 19.64^91
9,60988019.960617 Iq.649x^
3
4
5
9.6^0163
9.610446
9*^107x9
9960561
9.960505
9.960448 j
I
9.649163
9^649602
9^649942]
9.650281
7
8
9
10
9.611012
9.611194
9.611576
9.611858
9.612140
9.960392
9.960335
9.960279
9.9602-22
9.650620
9^650959
9,651297
9.651636
II 9*6 1242 1
X2 9.612702
1.3 9.612983
14 9.6 1 3 264
15I9.613545
9.960165I I9.651974
9.96010$
9.960052
9'9S999^,
9.95993^
9.959881
9.65iji»l
9,6526^50
9.653326
9.653663I
16I9.613825 9.959824
i7|9.6i4io5[9.959768.
9.959710
9'9i9^U
9.95959^
18
20
9.614385
9*6 1^6 5
9614944
9.654000!
9.^^4337
9.654674
9.655011
l9-^55?48
21
22
*3
%4
25
9.615223
9.615502
9..6J5781
9,61^060
9.61^338
9^9iPii9
9'9^9A^.^
9.9 5 94^5
9.9593^7
9*9^93 1<^
19.(^55^84
9.656020
9.656356
9.657028
26
27
iS
^9
9.616616
9.616894
9^^ ^7^^
9^6 174 fq
9.617717
9*9^9^5 1
,559195
591J8
59080
9-9590»3
9-^573^3
9,6576^
9.^58034
^.^58369
9.658704
o>3^^4^7l^<
5j
5^
5;
5^
0.3 s 1077
©•350757
0.350598
0.3 500^8
0*3497^9 5)
0-3493MJ4
0.34904^^3
0.J48703
0.34? 364
o.348oi6
^0
0*347688
0.347350
o«3v47oi2
0.346674
0.34^7
47
4«
4<
0.345999144
o.34565i|4i
0.345 32-5 W
0.3 4498 9Uj
o.344652l|«
0.544316
0*3439^0
0.345^43
0.343308
19*342972
V
o*342r636
0.34^301
9*341966
0.34*53*
0*341396
Ji
[Cp-fme \ Sme 1 '| C( Hr<g»g, fTa ngent |*
■ j. 'g * ' A.' g rrr
iW^
^ Degree 24* •
A \ Sine I Co-jfffe | |Tangcnt| C o-tant. 1
Iol9.^i77i7l9^959oi?| 19.^58704!
\
;i
;5
^•618004
9*6 18^81
9.^18558
9.618834
9.6x9110
9.958965
9.958908
9.958850
^.958791
J.95B7H
9M9171
^♦6 59708
9.660042
9*660376
57
59
40
9.619386
9,619661
9.619933
9.620x13
9.6io4S8
9.958677
9.958619
9.958561
9.958 Jog
99^8445
»^,66o7io
9*661043
9.661377
9.661710
9.66204 {
411^.610763
4^ 9.^xlo38
43^9.6^1315
44 9*621587
45 9*621861
9-958387
^958329
9.958271
9-958 1 12
9.958154
9.662376
9.662709
9.663042
9.663374
9.663707
46 9.622135
47 9*622409
48 9*622682
49 9-^»»95^
5019.6^3^29
9.958096
9*9i8o38
9*957979
9-9^79^^
9-957862
9,664039
9.664371
9.664703
9*6^5035
9-66 ^16$
1119.623502
5* 9*^^776
il 9.624047
54 9.^H3»9
f?l9.^»459i
9^57804
9.957745
9.957^87
9.957^*8
9-957570
9*66 S 6 ^j
9*666ot9
^•666160
9.667021
56 9.624^63
}7 9.625194
58 9.615406
599.^25677
^P 9j6i59.48
9.9575x1
9-95745*
9-957 J 9^
9*957J54
9.957*76
^.667352
9.667682
9.668012
9.668343
9.668672
0.341296I30
o.
o.
0*
o*
0.
0.
^»
o.
0.
o.
o.
o.
o.
o.
o.
0«
o.
0;
o*
o*
04
o.
o.
<?•
o.
o.
o.
o.
o.
40926
40627
40292
9958
9^4
^9[
28
»7
16
15
9290
8957
8613
8290
7956
7623
7291
6958
6625
6293
59^1
5619
5297
4965
4634
»4l
21
21
IIO
*9
18
n
I
M
11
Uol
4301
197^
3^40
3309
2979
^
264
2J>8
1987
1657
1317
1
1
\Cfhfint I Sine .. J , .| C(h*tf»g^|Tangent | irf
• • • I I ■ ' ^ — ' •* "' i n
f
.^ . — ■ u
Degree 25.
-- ■ ■■ ^^^^-^——
Mj Sine I Co-fme ' jTangcntj Cthtang. {
o|9.6i^948;9.957276| 19.66867x1
I
2
3
4
9.626219
9.626490
9.626760
9.627030
9.627^00
9.957099
9957040
9.956981
9.669002.
9.669661
9669990
9.670320
59
58
57
n
0.550998
0*530668
o*530339
0.330009
0.32.9680
7
8
9
10
9.627570
9.62784«
9.628109
9.628378
9*9569221 19.670649
9.956B62 I9.670977
9.956803
9-956744
9.62864719.9566^4
9.67x306
9^^1634
9.671963
0-5*95 5i|54
0.3290Z2I5J
0.328694
0.528365
0.328037
5»l
51
fo
II
12
'3
14
15
9.628916
9,629184
9.6294^3
9.956625
9.956565
9.956506
9.62^711 9«956446
9.629989I9.956387
9.672291
9.672619
9.672947
9*673274
9.673603
0.327709
©•327381
0.3270^3
0.326725L
0.326398/45
16
17
18
19
120
9.630257
9.630524
9.63079*
9.631059
9.631326
9^95^5*7
9.956267
9.956208
9.956148
9.956088
9.673929
9*674256
9.674584
9.674910
9.675137
o« 3 26070144
o*3»5745 4}
0.325416141
0,325089141
©•5*4765l4fl
21
22
24
15
9.631591
9,631859
9.632125
9.632392
9.6? 26 57
9.956029
9.9 U9h
9.^55909
9^955849
9.955789
9.675564
9.675890
9*676216
9.676545
9.6y6%69
0.324436 3i
0,324110 38
0.323783 3f
<>*5*3457 3'
o>?*5M ihf
— — - — ■ ~^^^^
26
17
28
19
30
9632923
9*633189
9.633454
9-^11119
I9.633984
9*9^^719
9.9^^669
9-9^S^o9
9.9^5548
9.955488
9.677194
9.677520
9.677845
9.6781^71
9.678496
0.322805
0*322480
0.3^2154
0*32.1829
0.321504
5i|
I Co-Ji«e I Sine !> (Co-z^fl^.l Tangent IM
I
Degree 25. ' ^
lip— — — i— — » - ■ III. , , . _..,.. ..I
ml Sine | Confine | [Tangent \C(Htang. I
3,019.65598415^.9554881 19.678496I
51
3^
9,634Z49
3iJ9-^g45i4
9.^54778
9.635041
9»^^!f3o6
9.9554^8
9.9553^7
9'9^U97
9'9SU^^
9.955186
9.678821
9.679146
9-^7947 »
$.<^79'795
9,68oi2o
?6
39
40
9.635570
9.635833
9.636097
9.636360
9636613
9«95Si2.S
9-955065
9.955004
9-954944
9.954883
9.680444
9,680768
9.681092
9.681416
9.681740
41
4^
4J
44
45
^.636886
9.^37x48
9;6374n
9.637673
9-^^79?5
9;954823
9*9547^1
9.954701
9.954640
9*9U'y79
9.631663
9.682386
9.682710
9.683033
9.,6JB3356
46
47
4S
49
50
9.638197
9;638458
9.638720
9.638981
9.639241
9.954518
9.954457
9954396
9*954335
9*954*74
9.683678
9.684001
9.6843^4
9.684646
9.684968
51
54
^5
9.639503 9.9542'i3
9.639764
9.640024
9.640284
9.640544 9.95 39^81
9»954Mi
9.954090
9.954029
9.68 5290
9.6856012
9.685.934
9.68'6>5 5
I9.686577
0.321504130
0.3 yi 179:29
0.320854 i8
0.320529 27
0.320205 26
0.319880 25
»
0.31955^1*4
0.319232 23
0.318908 22
0.318584 II
o«3 18260)20
Q.317937
0:317613
0.^3 17290
0.316967
0.3 1 6644
^9
tiB
17
16
15
0.3 1 6*3 2 1
0.315999
0.315676
0-3I5354
0.315032
H.
13
12
II
10
0.314710
o.3J43a8
0.314066
0-313745
0.313423
9
8
7
S6
$7
58
59
60
9.640^04
9.641064
9.64^313
9641583
9641842
9.953906}
9-953845
9-953783
9-9537**
9.953660
9.68689H
9,687219
9.687540
9.687861
o«3i3Jp2
0^31278^
0.31246b
0*312138
•J9^688i82|io>3ii8i8
4
?
i
.1
I
o
\C(^fmt I Suae I- 1 &-ii;f«|i. f Tangent (M
J
E ^^ec <?4.
ET
■ /
Degree ^6.
i««-M
Ml Siiie 1 Co-fim [ |Tangent| Co^aptg. \
o|9 64184119.95 t66o\ [9,6881^^110.31 18 i8|6o
9.642101
0.642^60
3 9.642618
4 9^642876
5|9-<54^i?5
9-95 5 59^1 |9-688f(5i
9-9S35571 19.^88823
9-955475
9.95 MI?
9-95??5i
9-^89143
9.689463
10.311498
lo.'j 11177
X0.310S57
16.3105^
9.68978 J |io,l*9>ijlii
5<
5^
57
5^
7
8
9
tio
^f9-^4^595l9-953i9o
9.6436-50
9.643908^
9.644165
9.644423
9.953118
9.953166
9'.953»<^4
9.953042
9.690103
9.690423
9.69074^
9.691063
9.6P13B1
10*309897
10.309577
I0.309258
10.308938
1 6.3086^9
119.6446801995*9^0
3 964519? 9-952'*5'?
9.645449 9«95i793
9.645706 9.951731
I
11
IS
14
9.69170P
9.69.1019
9.692338
.9.692656
|9.69_2_975
10.30S360
1 0*5 67 98 1
1 6. 3 07 662
10.307343
u
IP
49
4«
47
4^
17
18
1^
26
9.645962
9.646218
9.646473
9.<^467*9
9.646984
9,95256«l 19*693193
:
21
11
14
15
9.951606I
9.952544
9.9544^1
J^'9^^4Ig
9M7^l9\99SH^i
9.647494 9'!?5'ii?4
9.647749
9.^48004
9*6*48258
9.693611
9.695930
9.694148
lio.jo702S\4J
10.30^70614^
i<5.3b6388|4j
io.j<>6o7oUi
10.30575 ml
9.69 4 5 66 [ lo« 3 o 5 4 3 4)4C
9.p5ii3X
9.'95ii6«
9.952105 _
9.6 948 3 3>
^'.6"95toi
9.^5 5 »«
9.695835
9f9^-M!
10.3^05117 Ji
16.304799 j8
ie.~30448i ')?
10.3^04164 li
26
i7
28
29
30
9.^485x119,95^043
9.648766 9.951980
9.648010
9,649274
9951917
9.951854
9649527l9.95ir9i'
9.696476
9.6967B6
9.697103
9.697420
9697738
16.303530
16.303x13
ip«302)8^7
10.3015^0
ib.3oii64
i4
I?
LI'
1 Co-J? «e |- Sine | [Co-tang. I Tangent U
~ Degret.^3.. .
Mp Sine .iCo-fine \ iT%n.gp;it\ Co^ tart^, |
55
57
59
40
9*549781
9.65005^4
9.6501^7
9-650519
9.6 507 9i
9.951718
9.91166$
9*95 ^6oi
9-9^^9
99SU76]
9.651044]
9*6$iip6
9.65 1 64S
9.651800
9.65*052
9i698o5i
9r^9^]^9
9*698685
9*49900 1
9* 699 ^"16
9.951411
9*951349
9.951186
9.951^11
9.951159
4»
4a
45
44
45
9-^»5oJ
9-^5i555
^.651806
9.^55<557
9k6^^6^^
9.699947
3.700163
9.700578
#.7005.95
9.951095
9.95I032
9.950968
^.950905
46
47
48
49
50
51
U
55
9^^55507 9.950841
9.653558
9*653808
9.^f4c3r55
9.6545^9
9.^14518
9.701208
9^7015*2
9.701837
9*702 151
^•702466
9.654808
9^55657
'^j9-^55507
5419.^55556
5 519.^5 5805
9.950777
9.950714
f-950650
9-950586
9-9505^2!
9.^5 04 5S
9-950394
9^950330
9.950266
9*950202
9.702780
9.703095
9.703409
9-7037^1
9.70405.6
56
57
58
59. .,_
60I 9.6 56 3 47
9.656053 9*950138
9.656302
9.656550
9.'6^6799
9.704350
9.70466J
9*70^97^
p.70^290
9.705603.
9.950074
9.950009
9*.949945
9-949881
i^7o,$9^5
9.766228
9.706541
^.706853
9. #07 166
0.^02264^30
0.301947 19
0.301631- r8
0.30^315
0.300999
0.300684124
i^
0.3003^8 '24
0.300052 £3
0.299737 li
0.299422 22
0.29910^7420
0.298792
9.298477
0.298163
0.297848
0*197 5 34J
19
18
17
s6
15
0.297219 1
0.296905 13
0.296 59X 12
0.296277 11
0.295964 10
0.295650
0.295337
0.295023
01294710
0.29459?^
8
0.294084
0.293771
0.293459
0.293146
a29i834
\C9-jm I Sine \ [Co^^^ag, | Ta ngent jM
E 4
' ^ Degree27.
Ml Sine I Ca-//«« ITIangQitlC^iii2^. \
0)9.657047,9,949^801 [9.707166110,292? ^4[6
1
2
5
9-^57*95
19.657541
9«^4779o
;9v^rJo37
.5?.658i84
^.949816
9-^497 n
9.94^687
9.949615
^49.59^1
9^70747*
9.707790
9.708101
9.7084x4
-7,7o8726
10.192^5
jb.291210
Io.i9j897
10.291586
10.291274
5
5'
5-
619.65853119,9494941 'r9.7o9oj7i 10.290962
7 9M^in 9-9494^? ' 9.7<*9549 10.290651
8 9.^590*4
F9 9.^59*71
lo 3.659517
9.949 J 64
9-9495O0
9.9492-.? 5
9.709660 10.290340
9.709971 to.290019
9.710281 10.2897x8
50
II
XI
14
9.6597^?
9.660009
9.6^0 15 if
9.66050b
9.660746
»^"^
51.949170
9.949,105
9.949o'4o
^.948976
^.948910
9.710593
9.7 X0904
9.71 14 1 4
9.7115*5
97^836
l0.iy94O7'
10.289096
10.288785
io.28.8l47 5
10.188164
48
47
46
45
16
»7
18
«9
10
9.660991
9.6612^6
9.^61481
9.661726
9.661970
9948845
9948760
9.9487 1 5
9948^550
9.948584
zi 19.66 2 1x4
22 9.^2459
23 9,662702
24 9«66i947
15 o.66;{i9o
» ■»■
9.94845 J
9.948 J 88
9.948323
9948x57
9.J12146
9.7x2456
9.7x2766
9.715076
10.28^7^4
xo.2?7544
10.187234
io.286924
10,1866x4
44
45
4»
41
40
26 9.66 J 43 J
27 9.663677
28 9.^663920
2^9.664163
;o 9.664406
9.^48191
9.948x16
9.948060) .
9.9479?5
fi 9479^
9.7^5^95ltb,*2863o5
9.714005 xp,28 599 5
9.714314 10.285686
9,714624 10.285576
9.7x495^10.285067
— -H>— P^ ' III
^0.284758
10,284449
xo«2$4i40
10. ^8 3831
10.283523
9.7x5141
9.715550
9.7x5859
9.7x6168
9,7x6477
39
J8
37
i?
?4
33
?o
\ C(hfini j Sine j |C^^<««g.| Tangent pW
Degyee
d2*
Ml Sine \Co-fme \ (Tzngcv\t\CiHtaf!g.\
9 664^91
DT,9-^<^5J75
5519,665617
54
9.947863
9-947797
9.9477 1 1
9-947665
9-9^7^99
9.716785
9.7 1709 J
9.717401
9.717709
9.718017
10.28^x15
10.^8x907
10.^81598
10.181190
10.28198;
»9
28
*7
16
15
S6
S7
[3?
40
9.665858
9.666100
9.666^41
9.666 58 J
9.666^2,^
9*947555
9.947467
9.947401
9-947555
9.947269
19.718 2.15
9.7x865 J
9718940
9.719248
9719515
10.JL81675
10.281567
10.281060
10.280752
10.280445
14
^5
22
21
20
41 9.667065
42 9.667305
45 9-667546
44 9.667786
45I 9.668026
9.9471031
9.947136
9.947070
9.947004
9.946937
9.719862
9-72-0x49
9.720476
9720783
9.721085
10.280138
10,279831
10.279524
10.^79217
10.278911
19
r6
»5
^61 9*668266
I.7I9.668506
^819.668746
[4919.668986
]5o\9.669225
9.946871
9.946804
9.946738
9.J46671
9.946604
9.711595
9.72J702
9.XI1008
9.7**515
9.722021
10,278604
10.3^78298
10.2779.91
10.277685
10.277579
«4
XI
II
xo
51 9.669464
5a 9.669703
53 9669942
54 9.670181
5519.670419
?6
57
53
19
60
9*946537
9.94647.1
9.946404
9-946357
9.946270
9.670657
9.670896
9.67x134
9.671572
9.671609
^.711927
9.7i3»3i
9.71 5.5 3 8
9.713843
P7H149
10.177073
10.176768
10.176462
10.176156
10.175851
9^
8
^.
5
9.946203
9.946136
9.946069
9.946001
9«^4595.1
19-72.4454
9-7^4759
9.71^065
9.7*5569
9.725674
10.175546
10*175140
10.174955
10.174630
10.174316
4
5
If
X
1 Corfiie |. Sine | \C(htang* \ T angent |M
Degree 62. . ■
I
Decree 28.
Ml Sine 1 Oj-fine | |Tangent| co-t<i«g. | 1
o|9.67i«o9l9-9+i9J5i l9-7»5674|io.t74?i6|tfa
X
!J^7i«47
9.94I86B
9-7 '•597 9
io.»74o»i
5$
1
9.6710**,
9.94 iSoo
9.7»«i84
io.i7}8i6
5!
i
9.fi7il"
?-S457n
9.716(88
io.i7j4i»
57
+
9.671JJ8
9.94^6^6
9-716891
10.17} 107
5<
1
9-<7*79I
9.94 J S9*
^7i7«97
10.17180J
55
54
£
S-^TJoj*
9.94S!!i
9.71750*
10.1714??
7
9.67 J »««
9-9454*3
9.717*0)
10.171195
51
8
9-*7MoI
9.94s ! 96
9.7 1.8 109
10.171891
51
9
9-671 74V
9.945 J i8
i-94U6i
9.7*841*
10.S71587
51
10
9-^!»77
9.718716
10.171184
50
II
9.674113
9-945 19? 1
9.719010
10.170980
49
n
9.67444S
9-9451*5!
9.719J1J
.o.i7ofi77
Is
'3
9.674684
^.945058
9./19616
I0.170I74
47
'4
5.67491 9
9-944990
9-7i99^9
10.170D70
46
1*
9-67 UU
9■P4■t9l^
9-7J01I1
lo. 1*97 67(451
f*
j.67ij8j
9.944854
P'7Jo53f
10.1*9454
44
17
9,«7(tftJ
9.94478*
9-7Io«j8
10.1*9161
41
iS
9.<758S9
9-944718
9.7 J 1 141
k 0.1*8 8 59
>J
♦.«7«094
J,944<fo
p'n'44!
10.168556
41
10
9.671! J >8
»■ 944581
9-73 '74*
ia.i68i54
40
ai
5.67*561
^9445I4
9-7! 1948
10.167951!
39
II
9.676,96
9.94444*
P-73135'
10.167*49
3>
*3
9.«77*io
9-944 J77
9-7 J 1*5 1
io.»67J47
10.167045
lio.»6674j
37
i4
9.677,64
9.944 J 09
9*7J»9I5
3*
tl
9-*77497
M44141:
9-7 J 1 15^
ii
»6
9-6777JI
9-944171
9-7J3558
10.166441
J4
»7
9-^77 9C4
9-^+4 '04
9.7 J? 860
10.166140
}i
tS
9.67II197
p.9440'«
9.7J4i6i
Fl 0,165858
\\
t?
9.67 84 JO
9.9439*7
9-7M4fij
10.165537
{1
If.
9.678663
P-94J898
9-7347*4
io.i6Sij6
Jo
1 C<K/?«e,
Sine 1 ICp-fjng.t Tangent |m|
>e£
'-
'
■««i
r— — •
Degrcc28.
M| Sine | Cthfine \ |TangentlC o ^j;f|;, \
110.678895
9.^7 9 J ^o
9.6795^1
9.679814
S
3
54
3^
9.94^850
9.945761
9.943614
19.943555
9^755562
J9,7J5668
9.755968
9.756169
io*ft64954
iOk»^4653
io*i^4n»
10.16403 1
io.»6^7}i
2^9
»7
x6
57
146
41 9.68Ui3lip.945i4i
9.68605^)9.943486
9.68 02 S8
9.680519
9.6807^0
9.680982
9-94H^7l
!9-9'43348
19*94 J ^79
>94?iio
!^736$7olio.»6}4jx)
|^73687o[io*i6'3t36
io.x6ft8x^
10.1^15x9
10.1611x9
9.737«7J
9»75747i
9.7^77.71
*4
XX
XI
41
4J
44
45
9.«83t443
^.6«4<7J^
9.681904
9.68^x135
9.943^571
9.943ox>3
9.943^95?
9.94x^64
9.738071
9.738371
9.738671
9.718:97 1
9.739*71
ic.x6i9x9|i9
io.s^i6<9 18
to.^i3x9 x7
Lo.x6d^x9ii5
4«
4^
4^
5^
9.68x365
9.68x595 9.94^*5
9^8x8^5
9.683055
9-941795
9.94i656
9.94x5*7
9.68^1849.94x5x7
•9.^39570
.9.739370
9.740169
9*7 4x246 8
9.740767
5i|9.6«35i4l^.94iv44«
9.^83^43 9.94x378
1CSX66430
io.x6ol^
10.15983 1
io.x5955i,
to.x59x3^|rb
-
H
It
XI
52^
53
54
9.68 J 9fi
9.^^10 1
51I9.684436
9.94x.3x>8
9.941139
9.941x69
9.74x066
9»74X565
9.74x^4
9.7419^2
9.74xii5x
10.1589341
10*1 5^6(5 8
xo.i5*1 J*^
io*iffos&:
«o.ij77}9l i
{
5^
5/
58
59
66
9.68465i(
^.694887
9*6*fxx5
9.68 f 343
j;68f5?i
9.94x099
9»94iox9
9-94*<5S9
^.94l6€9
9;94x8i9
9*74i559
9.741858
9.743x56
9'743454
9*7 437 51
I0.x5744^
xdiit7t4i
10.156844
ro.156.546
10.15614^
4
\ \ Cchfim \ ^nc \ \C (htang4 \ Tangent |M
Dcgtccdi.
f
29,
Ml Sine \ Cthfim \ lTangcnt| Co-tMg. \
1
%
I
4
5
9.68 575^9
9.68^017
9«686i54
9.68 6481
9.686709
P-9417491
9-941^79
9.941609
9-94X559
9.941468
9.744050
^744548
9*744645
9.744945
|?-745i40
10.&55950
io.*S56si
xo»55355
10,155057
i.o«x5476o
7
8
xo
9.68695619.9415981
9.687x65
9.687589
9.687616
9.687842
9.9413^8
9.941*57
9.941 187
9.941116
9-7455J8 10.254461
9*745855
9.746152
9.746429
I9.746726
10.254165
10.25^868
10.253571
10.253274
II
»4
15
55
5«
57
5«
55
54
5}
51
51
5o|
9.688069
9.^^88295
9.688525
9.688747
9.688972
9.941046
9.94097 5
9.940905
9.940854
9.94076 5 1
1619.689198
17 9.689421
18 9.689648
19 6.689875
10 9.690098
21 9.6905*5
22 9.690548
^5 9.6907 7 1
24 9<6^996
*5 9.^12*2,0
9.940695
9.940622
9.940551
9^940480
^ 9^409
9.747025JX0.252977
9.747 5 1 9I 10*2 52680
9.7476I6I 10.15x584
9.747912110.252087
9.748 209I 10.1 5 1 791
45
4«
47
4^
45
9.748505
9.748801
9.749097
9-749595
9.749689
io.jrSi495J44
fo.25.i199 45
'io«25o902 41
10*^2506/27 41
io«>5io5.ii 40
9.940)558
9.9402^7
9.94Q!* 9^
9.940,12^
9.940055
9-749985
9.750^81
9.750576
10.250015
10.2497 1 9
19.249424
9*7 5 1 ^^7
9^50872 la.249128
10A48S 3 5
59
5«
57
5«
55
2^^9,691444
9.^1668
9^1^1.^92
29 9^692115
3oj19.«92?59
i7
28
1 9-^5 9981
9.939911
9.^59840
9» 9 59768
9.9 5 ^%7
19.75146 a
9751757
9.75205Z
9*7 5*547
9.752642
10.248538 34
10.248:^43 53
10.247948 51
10.24^659 5!
10.247358130
\^2:jmt I Sinp I {Co^ang \ Tangent |1W
Degree ^o.
ppwg.
/
, — -^ —
Degree 30,
M
Sine I Co-fm 1 iTangcqtl Co-t^ng. I
0{ f. 69a 970! 9.9 J7 mt_l 9'7^^439' ^g! ^?^^^M^o
» 9-^99497
f 19.700061
9<r937458
9-9373 »*
9-937*38
9*937?^5
19.76x751
9,r^i3[i4
9.761^96
19,76x897
10.137977
10.^57686
I0.1J7394
io.i37lQ5
59
57
56
51
7
9
10
9^700x80
9-7«P498
9.700716
9i7P«>933
9.7QS151
9,937091
9-937o»9
9*95^945
9.936171 »
9*91^199\
II ' 1 — r— — ■
9.763188110.1368 IX
9.763479
9.763770
9.764061
9.76435 a
II 9.70 »f 68
II 9.761185
13 9»70i8oz
14 9»7P*oi9
1519.701x36
161^.70*452.
|i7 9i70i669
^18 9.703885
9.9^671$
9.936651
9.936578
9,936505
9.936431
9.764643
9-7^4933
9.765x14
,9-7^5514
9,765805
10.1365x1
la 136x^0
10.135939
10.13564815^
54
53
51
IO.X353 57
10.1350^7
10.134776
10.134486
49
4«
47
4*
iQ.x34i95l4f
»9
9.703101
9.703317
'9.93^^57
9.936x84
9.936x10
9*93^M^
9.9 3 606 X
XI
XX
24
fi5
9»7«^353?
9*703748
9.703964
9.704179
9*704395
9.766095
9.766385
9.766675
9.935988
9*93 59^4
9.935^40
9«9357$^
9-935^9*
9*7^7 545
9.767834
9.7681x4
9.768413
9.768703
io.x539o$|44
io.x33^i5 4J
10.13331x5 41
10.133035 41
10.131745 140
io.a3i451|i9
10.131166138
10.13187^
10.131587
10.131197
17
18
1619.704^10
9.7048x5
9.705040
19 9*705i'54
30 9.70^54^9
9.935618
9*935543
9.9354^9
9'9^^^9S
(9*9353^0
37
3^
}}
134
3^
io.i3043ot3i
9.76899X/ 10.13^008
9.769X81U0.130719
9.769570
9.7^9^59
10.130141
■9.7701 481 10*1x98 5 X
31
30
.\C§^ 1. Sine- | \C(htang. ITangeiit |M
^^mm
ee 5y.
«HK
mmik
Degrt
ec 30.
« ■ ■< I ■■ ■ « ■ 11- ■■ • Il l II ■« i>.ii.t jji- " - ■
Mj Sine I Cfhfmt \ | Tangeotl Co^ang^ I
^— ^— I i B li i M » ~*— ^— ■* ^l»^».^»»^^ I I I I ■ I » M "" I II I I ' III III ■
31 9.70568^
Ji
9*70%^97
J3;9.7©^iii ^•^^5097
341^.70^5*^9.9 J 5o*a
55
9.7 of 5 5 9
36 9,Voi^75B
9-9U948
9'77»437
9.770716
9-77 10^^
9*77 '^0 J
^.77 1 $9*^
io.iz9$^5 X9
10.2 19 £7 4 18
io«ii896$ 17
xo.tx8^97 26
xo«iiS4o8 25
57
J9
40
9«7 0^967
9.707593
9.707606
9*95487 5
9954798
9,707i8<^ 9^954723
9*954^4^
9.954574
9«77.i88o
9.77**^8
9.771.456
9.772745
9775055
I0.<ft8l2p
I0.227832
io,227545
10.227255
10.12^6967
^5
22
20
4I;
41
45
44
45
9.707819
9.70803*
9.70*14^
9.708457
9.708670
9.954499
94954414
9*954549
9-954i7'4
9-954199
9*7753*1
9.773608
9.773896
9.774184
9-774471
iQ,226679
I0.22639X
10.126104
fo«ii58x6
ib«ii55'i9
19
17
16
9.708882
9.709^94
9,709306
9*709li8
5019.709730
46
47
4^
49
9*9 5 4 II 5
9.934048
9*91197 ^
9.1955897
9.774759
9*77^046
9,775555
9^775621
9^775908
10. 12 5241
X0.124954
io«ii4666
x p. 124 3 79
10.214092
X4l
15
11
?i
lot
5
51
55
54
55
1.9
«7 09941
9-7i«l55
9*710364
9.710575
9.710786^
9^955747}
9.955^7i|
9-^95559^
9.955510
9.95^5444
9*776195
9,776482
9^776768
9*777055
9^777 541
10*113805
io.2i3 5i8
1 0.1 2 ji 31
10.111945
X 0.121658
9!
8
7
6|
5
5^
57
58
59
^o
9*710997
9«7Xi2o8
9.71x418
9.7x1629
9.711839
99555^9
9*955195
91955117
9-.935141
9^933066
JI J ■ i.^
(9.777:6:28
9.777915
9,778201
94778487
xo.x2i37i| 4
xo.i&ioSf
i^<22i799
xo.22i5r5
9.7787741x0.12 1116
X
o
I Co^^e I . Sine {[Co-t^ng. | Tangent iM
"— *— **■— iwp*<w>y*«.>i 1 1 - ' " ■■■'■'■ II I . II o ii p . t i— — .1 1 1 ■ ■-■1^
J£:
6 9-7^0^8
7 9.7iJJo8
9 9.7U716
iAM^ah
Degree 31,
M| Sine | Co-fine | jTangcntJ C(hiang\
o|^7ii8^9|9,9^3o66| 19.778774! io«ixi^x6|6 o
X
4
9.711049
>.7iii59
9.tii4^9
9.711^79
9.711889
9.931990
9.93 »8j8
9.931761
9^32685
9.779060
9 -77934^
9-77 9^ i^
9-1799^^
9^78oip3
9.931609
9.93*533
9.931457
9*93*3^0
9931304
tr~«5"
I o* 1109401 59
io.iid654
lo.izoftfS
lo.iaooSi
10.119796
58
157
9.780489
9.78077 S
9.781060
9.781346
9.78 163 1
10.1X951X
19.119115}
^6.118940
io.£i8554
10.218369
5^
55
54l
53
51
51
|50|
11
9.714*44
9.951117'
9.781916
11
9-7 » 43 51
9-931151
9*781101
M
9.7.145^1
9.931074
9.781486
14
9.714769
9.951998
9.78177 1
15
9.7M977
9,95 1911
9.785056
10.118.08414^
IO*2 17799 48
<o<ii^5l4 47
10.1x7229 46
10.116944 4f
16
17
t8
19
10
9.715*86
9.715394
0.715601
9 715809
9.716017
9-9318451
9.9317^8
9.951691
9.931614
9.9?t557
9.785341
9.785616
9.7859x0
9.784^95
10.1x6659
to.116374
10.2x6090
10.2x5805
9 7844791 10*1155x0
441
4J
41
41
140
21
11
13
14
9.716114
9.951460
9.784764
9.7 1643 1
9.951585
9.785048
9^71^659
9.951506
/
9.785331
9.716846
9.951119
9785616
9.717053
19.931151'
9.785900
10.115136
10.214952
10.1x4^68
10.214384
io.i 14099
391
3«
3^
35
16
17
18
19
Jo
9.717159
9.7174.5^
9-7^7^^
9.717869
9.718085
9.931075
9.950998
9.950910
9.930845
9.930766
9.786184
94786468
9.786751
9.787056
9.787519
10.1x381^134
10.11353.* 33
to.2i3»48^ 31
fo.it i9i$4 31
[to iii6Sx 30
1 Cch-fine I Sine | \C(Htang. | Tangent \tA
D«ree j8i
— >— *>i>ili lilt I I lllAfli Wff'iU\im\
MMtei
Pc grec 32.
W Sine ]Co-fine \ |Tangcntj CoHang. I
0)9.7x41 io|^9%842.o| '9>79 5789i^^*^04yxi
1 9.7144^2-
1
3
4
5
9.714^14
9«7 14816
9.7x5017
9.71U19
9.9x8341
9.9x8x6x
9.918x83
9*9x8104
9,9x80x5
7
8
.9
to
9.7x54x0
9.7X56XX 9^x78^
9.7x58x3
9.7x60x4
9.^*7946
9.9*7787
9J9X7798
9.9x76x8
[9.796070
9.79^551
9.79663 X
9,796913
9-797474
9-79775^
9.798036
10.X03930
10.X03649
xo.x03,368
IO.X03QS7
io.xox8o6
9.798596
Xo.xo2.$:^x
xo.xoix45
10.^0x9^4
9^798 3161 XO.XOX684
X0.XOX4O4
til 9.7x64x6
ix jp.7x66x^
9.7x68x7
9.7*70x7
^3
t4
t5!9-7J'7i*8
9^*7 549
9.9x7469
9.9x7390
9.9x7310
9.9*7*?
16
»7
tS
»9
9.7*74*8
9.7*7^*5
9.;^*78x8
9.7x80*7
10 9 7*?**7
XI
tf
*4
*5
9.7x84x7
9.7x86x^
9.7*88x5
^,7x90x4
^.7x9x13
9.9x715
9.9*707
9-9*^99
9^9*^9'
9.2x683
«■ II >
9.9x675
9*9x667
9.9x659
9-9x651
9.9x643
x6|9.7X94xx
X7 9.7x96x1
x8 9.7x98x0
t9| 9.7 3 00 1 8
$0)9.7^0x16
* » * . ' ■■
9.798877
9-799M7
9*7 994 J 7
9^7997^7
XO.XOIIX3
X0.X0O84.3
IO.XOQ563
94799997lio«xooOa3
60
59
58
57
5^
55
54
5J
5*
51
50
49
48
47
46
45
9.^00x77 Uo** 997*3 44
9.800557 10.199443I43
9*800836 xo«X99X^3
9*801x16 10.1^98834
9^801396 10.^98604
9.80x6751x6.1983x5
9,9x635
9.9x6x70
9.9x6190
9,916110
9.91601 V
9^801955
9480x134
9#8ox5x3
9#8ox79x
A ■ I .1
9.803072
9.803351
9.803630
9.803908
9.804
10.198045
XO.X97766
iax97487
XO.X 97x07
4J
4«
45
38
?7
J5
90a i
187I1
xo^X969x8,
xo»X96649
.10.196370
X 0.196091
0.1^58 X?J
I
\Co-(ine ' ( Sine ' j \Cfi'tang^ IX^ngent |.
f—
Degree 57.' '
i
Ml.Sine... 1 Cr-_gffFX-]Tangcnf| fcerfg/^.-j
3f'\9^7lo:i'^b9'-(-.Qi9\ j9^^hi7\lo.lk\*]i'U °
9.7 J 1404
?7J'po'
4e|g.2l*'jing9^5;
9.7J1JI7
9^yfit*4
9-91S70?
.£116 1_6
^1804466
9(864745
9.805 iSi
9»!S4S
5'.9HjS4
Mn>4^
9,911:066
?j9H97S
9.9^489?
91914316
9!>W4.^
9IH66;
iilM9:
9'734S3|
9-y343V^'«9i4J"
- ■,■■,■ ^9*4146
?-73Vy^d9H>64
5J-9*4ttBj
9.7tU^Wi40o:
9-7ji3i'*
9.7in^i
Sfc9ij9i9
!l?»375 5
■pi!*?!
9.9tn9i-
9,867141*
9,96^86S
2j68j6i
;i
[Sic!*
StbB57
9lSti.
j8i
J!!J4
'<!•,■?;■- 1"!
^E|
p.tii
IO.lg86j9[
io.i?77J9
o.i»74B{ )
,- .. Degree' 57; ,_„
Ml Sdc \ Co^ \ tTangentl Co-tang. [
12
I 9»7i^io9\9^%iio9
^{9-71^497 9'9H^^7
i 9-1l^^9\ W13J4J
l97J70$obi9x5i8o
J MJ7487 9*9»jox6
*i5>-737jf I 9*9^^Hi
5^ 9.7?7»?4 ?.9^»Mf
9.Tii794
9;S|J070
9*^»H47
9.8130x3
9>^'3^99
10.187 xo5| 59
10.186653
10.186^77
10.186101
9f^»4X7j
9.8x4452
9*814718
9^815004
9.<i5*79
10.1858^4
10.185548
to.x8527x
xo»i8472o
^T 9-77?^f i}9.9**^^
^* M??4|4 9?9»itfp|
^3 ^.758pi7- 9i9i*<^o
^4 9.7iS«>q 9l9*»4J^
Af^9-7392H]9l9"J5f
16
1x8
'to
9?7Jf^^S9f9^^%7^
9'7i9i9^,9^9nhh
i'7mh 9^9i\io6
9'7JJ>783 9l9*>ox§
f>739fl7d9 j9^j940
r I
J
9^^iS555
9^8x5^jx
9*816x07
9»8;638x
>8i66$8
5*
51
12
X0.I84169
xa.it2893
i6.|8|6i7
io.l8£|4x|4j
47
4^
■9.8169J3 10.1^30^
9f8j7»?9ri<i^>>79i
9^817484 ik^xSaS^i^
4^
4j
4»
9-7404^7l9»9*i«^f7
.MmS'9 9'^9^^774
9.74#!4;^ 9^9n6p7
*5
1^9.74x1x1
^9o[J9
»7 9.7*M>^9-9»JJ57.
?^ 9.74^07^ 9«9»i »74
^9 9'74>^9^ 9*92) 190
?ol5«74ji99l9-9i3Lio7
9.^x1441
^m^^
9f8x88^pl^.i8|>4o
9^5 19? J 5 to.x^c>8^j
9igl94iol^oa8p.59o
9f^j9^$4jiflbi?pjjj
9f8.>9959V<^»36o4i
9.8xo5p8 IO-V94P2
9.8x0783 i!0.i?9i^7
3<{
I
j Co^^i ,1 Sine . 1 . \Co''iang^ iTangcnt I
'" ,' Degree :<6*~^ ""
D^KC 33- __ - -
W| Sine -jCt^tne 1' iTahgeritl .Co-»*»ji. j '
•o 9-74i^9\9-9^'ii07t:i9^^7^iUo.ijgiii[isi
■ 1 9.741080
9.9ii<^xj
9.Siio^7
>«'»75J4j
^?
[I 9.741171
9.9^6919
9^8i.;ji
13 9i**»4S>
9.(jio8(J
jja-iifid*
iip;i78j9^
IT
14 j..74*6<x
!
I0.178U0
[5
9i74i«4i
?.9.to688
flSJiiU
> 0^1-77 84^I(
(6
9.74 JO J 1
9.91061)^
9,811419
i0.i7flT^
U
17
?i74Uij
9i9i05io
9J81170}
10.177197
»1
t8
9.7414"
9-9t°ii4
9J»"977
I0.i770i'3
*i
\<>
9j8ijifo
i-t.(7f?3^
♦0
9-74J791
9.9ioi<;8
b-
9.*?:jli4
1 9.1764^
It
♦ '
>-74J99^
9.910 1 84
9^813798
lit. 176-101
M
*i
9-744J7'
p.B>407'i
T4.f7<5i«
♦ ?
9.744361
9.5(10015
S
t1
9.7445 Jo
9.9" 99 J 1
i
♦ <
9-,7447J9
9.919846
i
46
9-7.449^8
9.9I9761
9
47
9.745117
9.919677
9
4«
9.74SJ06
9-9^9^91
s
4?
9-745494
9.9 '9508
s
50
9-7+568J
9.9'9»»4
i
51
9-745871
S
s
9.746148
{
f5
9-74<fi»4
s-,„,.
T«
9,746811
9.918915
9.9»P<J0
9-»l7B97
10.17 11 OJ
'
57
9-746999
9.I18.76
9.n844i
to. 171*^0
1
58!9.747'87
9. 9 '8744'
10.17155*
f 919.747^74
9i9iS<(59
9.C1871J
10.17 1 1^5
1
60
9.74756*
9.9181174
9.8 1« 987
to.J.71011
I 0-P»e|; Sint "1 .1C*-(OTg. Tangicnt.
K.
_Dpgtee5«.
F 3
9-7477,4? 9^'
9«7479J6
P-748»*J
J.749J19
J.74868J
?,74a37o
9.7490 s*
5.918404
9.9(8118
9-9i8*i!
9. 9'a»47
9.74PS^» 9^y8o)
»74y4J^
?-74?*iTl9.
9.7«Sai
9 745ijlS6
9,7Soi7j
9-9>7S48.
9-9»7-4^-2
9-9'7J7*
9-7 5,0 W.
9.7S07J.9
ii-7SD?»4
9.7^84
!l.7ii^jB
9-7^013
^7i»A07
971
S|'7S*S76
9,7jJ76o
3-7n944
^■7ni>8
9-91797*
9.91789:
9^917719
9.917104
9.917
9.9170J1
9.91^945
?-9'S77!
9.^i66S6
SLyi65i4
■9.91*417
... «J4'
91^16154
9.pi6itf?
9.91*080
9-fM9y 4
9.8 106:
9.8 308 9j
9Jijii6i
.|J8 11437
9.>Sji7a9
9^ i.9iSo
9^1?IJ
9*JQ077
9^31981
9.8 J" «
9.631515
9-BJ179*
9.3 J 506a
9-8IJJ39
9.Ui6ii
9.^3881
9P341S4
9-^344iS
9.814***
(34967
.fijSS09
9-t3^r
9.l!^,iL,
9.»j6l91
9.<;f;S*4
"3'/'J4
10.170740
0.170^^
'o.i£99ti
o.'*9*5i
10.1^9379 fl
10.169106 f;
iO.L6Sg]4
10.16S1.
io.tfiSoi9
O-X 67747
0,167 47 ^
*j67io4
io*i66£6q
1 0.1 ££3 83
10. 1661 18
io.l6;84£
io.i6i575
1^5304
10.16 Jo J 3
- 0.164761
0.1*44^ J
id.i65<
10.1634
lO.l^^I
tfiB
I Ca-jfit 1 • _ Sine , t T C<-f ^wig. j Tiange
A\ Sine | Co^int \ iT^ ent| Ca-tiO j^.
9.7^jii.8 9-9i^99M |p-8}7iUl»o i6xi66\ ; .
9-7 n I
?.7SJ495
»-75J*79
75404^
9.7i4»!
9-7S44i
9-7^4778
9.315907
9.91(8
9.9>?7JS
9.9>J^4*
9-9»!559
P-8J7401
9.8J767
?9J794*
kajg -
\9.»iH97
9-9>5j85
9.915197
9.915110
9.P15»»3
9-7fI'43
9.7I5J»5
9-7lI!°8
9.755630
♦1
46I9.7560S4
4719.756136
49 9.7 5^+18
49 9'7S*^<»
5019^756781
9.914948
lg.?u8Bo
iB-91477}
,[9.£i4685
9.914597
9.91451
9.91*4:
9.914IJ4
9-9H^4^
5il9-7l6si6?|
5* 9-7^7 "44,
5! 9.t57?«'*
54 9-757507!
5519.757688
,9-9x4070
|9.yij9li
9.911854
9.9 1 {806
56I 9.757869
57 9.758049
5E9.7i8iJi
59975841
60I9.7J859
19-8j*7Sr
9^1? 9017
9-8i9>97
9.8J9563
.P.'i9M8
o.i6ii4j
0.16097^
i6o4ji
i6ol<i
19.840108
9.840178
]9.>4fi647
9.I409J7
|:9-i4't87
IP-84H57
^9.841716
9.14199^
l9,843.&66
\9->^'>-n^
o.i6t595
o.i6iji5
o.i6ro54
0.16.784,
o.'6i5i 3 :
10.159S9;
0,159611
0.1S9JJ:
0.15908)
53I4J
10.15817J
158004
I577U
157461
I9.841J04
9.91J718
9,9ij6j.
9-9»?54ii
9>9iJ4ijl
9^91^4!
9.8+4 1 J
9.844410
p.«446B9
9.844958
9-84i*i7
10..57.-9SI 9
■- -56916 -
56657
:56 -^
10.155849
i_o.iS5j8i
IO.I55JI
io.i55o4»'
10.154 774
t Ca-f m i Sine | \CMa71g. 1 T a ngeht |
De^ 55.
F^
;; Degree 35.
Ml Sihc I pthfint \ iTangcntI Co-sang. ]
I
I 2
3
4
I 5
7
8
9
o
I
9»75859»i9«9in^4| l9>?4St^7i
9.758771
9.758952
9.759>3i
9-7 593**
9.7 5 9491
9.915x7^^
9.91 3 187
9.91J099
9.9x30x0
9.912921
9.845496
9-8457^4
9.84^033
9.846302
9.84657Q
9.759^71
9.759851
9.760031
9.7602x0
9^.912833
9.^x2744
9.9x2655
9.9x2566
9-7^0 1 90 9'9«*477
9,846839
9.847X07
9.847376
9*847^44
9.94791 3
9.76«5^9
2J9.760748
9.7^0927
9.761106
9.761285
9.9x2388
9*9,m99
9.9x^2x0
9*9 121 2X
9.9x2031
9.84818 1
.^848449
9.8487X7
9.?4?985
9.849254
9.761464
9.76x642
9.76x8^1
9.761999
9.762x77
9.911942I
9.9x1853
9.9XX763
9.9x1674
9.9x1584
9,849522
9.849789
9.850057
9.8503,25
9.850595
i
5
9»76^tS^
9.7^*534
9.7627x2
9.7628S9
9.763067
9-9^149^
9.9x1405
9t9»iP5
9.9x1^26
9.9x1x36
9^7^314519 9* J04^
9V7^342'2 9.9x0956
8}9'7^3599 9-9io866
-9 9-7^3777 9-910776
?p|?!Zli?l49'9io686
9.85o'86x
9-8 5 U 28
9.851396
9.85x664
9-85X93I
9.852x99
9.852466
9,85273;
9.853OQI
9>85326|
o.
ou
o.
o«
o.
o.
OW
Q.
O.
O.
O.
o.
o.
o.
o.
o.
o.
o.
o.
o.
0.
o^
o*
o.
o.
o.
o.
o.
547741^
J4504
S4*35
$39^7
5?4i9
5316X
53892
52^M
?i35^
52087
^5
5«
57
5^
55
^
5a
51
50.
5x819
51551
5x183
5x015
50746
i
47j
4^
45
50478
502x4
49943
49675
49407
44
4J
41
41
40
39
38
37
3^
^35
4780X 34
47534 33
47*67 31
4^999 31
4673 1| 30
49 1 39
48872.
48604
48^3^
48069
I Cffifie I Sine ( \CortMg, | Tango it jM
Degree 35.
■ ■ I I ^ ' ' ' . . — .-r^- I
A\ Sine I Cchfine \ \ Tangciit[ Co^tang^ \
■^1 II i .ii- I ■ I Ml I I I I II!.
;4
9.7641 ji
9.754308
9.764485
9.764662
9.764838
9.9^x0596
9.910^06
9.910415
9.910135
9-7^5oM
9.853801
9*854069
9^854336
9'gU^o?
57 9'7^5X9i 9-9«oo54
^8*9.765367 9.909963
59
♦3
44
9.910144
9*7^5544 9 90937.?
9.765710 9.90978^
...^
9.765896
9-766071
9.766247
9*766413
45 9«7^^5$8 9:909328
9.909691
9.^09601
9.909510
9.909419
9.854870
9.855137
9.855404
9.855671
9*8559;?
10.146465
10.146x98
10145930
I o, 14 5 664
10.X45397
»7
i6
15
4^J9«7^^774
47l9»7^^949
9.8 56104
.9.856471
9.856737
9.857004
9.857170
ior.i45i}o
IO.I44863
10.144596
10.144319
1 (5.144063
11
II
10
10.143796
10.143519
10.143163
10.141996
10.141730
19
18
X7
16
15
48
49
150
51
5*
^3
54
55
9.767114
9.767199
9-7^7474
9.909 a 3 7
9.909146
9.909055
9.908964
9.9©8873
9-8575J7
9857803
9.858069
9.858336
9.858602
1 0.142463
10.141197
10.141931
z 0.141664
10.141398
9.767649
9.7^7824
9.7^7997
9.768173
9.7^1348
I III a,\ I
14
13
XI
IX
X6
[5^
57
58
59
60
9.908781
9.908 690
9.908599
9.908507
9.908416
9.85^868
9.859134
9,859400
9.8599?*
10.141 X^ll^'l^
10.14086^
10.140600
9.859666 10*140334
10.140068
7
61
5
9.765511
9.76%^!
9.769045
9.769119
9.908 3 24
9.906233
9.908 141
9*908049
9.907958
9.860198
9 860464
9,860730
9.860995
9.861261
10.139801
10.13953^
10.139*70
10.X39005
10.138739
41
3
1
I
01
■I Confine I Sine | | Co-tang. | TangeiiClM
I U"
Degree 54.
Degree 3^,
M) Sine I Qhfine \ \T^ng'tnt\ Co-tanf^. i
I
\
4
5
9.769591
9.769566
9.769740
9*7^9^1?
9.770087
9.907866
9-907774
9.907682
9.907^90
9.907498
7
8
9
Uo
9»770z6o
9»770455
9.770606
9^770779
9*7709 fi
9.907406
9.907 J 14
9,967211
9.907 129
9.9O70J7
■•— *
9.86 15 27 j
9.861792
9.962058
9.862^2;
9.861589
9*862854
9*86; X 19
9.863585
9.863650
9.863915
ij
\%
14
M
17
18
19
to
9«77'i*5
9.771298
p.771643
9.771815
9.906945
9.906851
9.7 7 1 470 9.906760
9.906667
9.906574
9.364180
9.864445
9.864710
9.864975
9.865240
9.77^987
i>.77ii59
9«77iJ5i
9-77*503
9.77*^7^
9.906482
9.906389
9.906296
9*906203
9.936111
9.865505
9.865770
9.866055
9,866300
9.866564
1* 9*77*847
X2.- 9.7730X8
15 9-773I90
»4J 9*77 33^1
»5i9*7735JJ
9.9060x8
9.905915
9*9058 3 >
9.9057 J 8
9.905645
6.866829
9.867094
9,867358
9.867623
9.867887
26
»7
.8
i9
JO
9-773704
9^773875
9-77404^
9.774217
I9.774388
9- 905551
9.905459
9.905365
9.905171
9-90 5 1 79
9.868152
9.868416
9.868680
9.868945
9.869209
0.158759
©•I 5*47 5
0.158208
©•^3 7941
0:1 57^77
0.X574XI
0.137146
0.156880
0.1566x5
0*156550
0.156085
O.X35820
0-155554
0.135289
0.135014
c^i34759
6fl
55
5«
57
5<
54
5J
5J
51
5fl
4^
0.134495
o.i3423o|4]
0.15596543
0.155700
0.155456
0.133171
o.X53^9o6
0.152641
0.151577
•^152113
O.X 51848
0.15x584
0.131520
0.15x055
0.130791
I Co^fim I Siiie | | Co^ang. \ Ta ngenTj]
De^r#c 55.
wmt^m^bt
Degree 3^.
HI Sine I Confine \ iTangcntj C(h4a9i^,\
28
9-774558
9.774719
9.774899
;4J9-775o70
r5 1 9-7 7 5 HO
J7
j8
J 9
9.905085
9.904991
9.904^98
9.904804
9.9047 1 »
9.86477 J
9.8673 J 7
9*870001
9.870165
9.870519!
9.775410
9.77 5 5B0
9-775750
9.775.910
9.776690
9.9046 17 1
9,904515
9.904419
91904335
9.904141
9.870793
9i87lo57
9t87i3ii
9.871585
9.871849 1
4i|9.^7^i59
4i| 9.776419
43|9-77^598
449.77^^
45|9-77-^937
9.904^47;
9.904053
9t9oJ959
9^903.864
9 *903770
9.871111
9.87*37^
9.871640
9»87i9o5
9873167
o.
o.
o.
o.
o.
o.
o«
ov
o.
o.
o.
o:
o.
o.
o.
30511
30163
19999
19735
19471
191P7
18943
18679
18415
18I5I
17888
17614
173^6
1709^
16833
17
16
14
13
11
11
10
^9
18
17
16
£5
14
II
Xx
46 9.777106
47 9-777175
48 9-777444
499*777^13
50 9-77778»
51"
5i
53
54
55
9.903^7^
9»90358i
9.903486
9.903391
9.903198
9,873430
9873694
9-'73957
9.874110
9.874484
o.
o.
o.
Q.
O.
16570
16306
16043
15780
15516
9.777950
9.778119
9.778^^87
9-77^455
9.778^13
$.903103
9.903108
9.963013
9,901919
9*901824
9.874747
9.875010
9.875173
9.875536
9.875799
o.
o.
o.
o.
o.
151531 9
14990I
14717
14464
14101
56
57
58
59
4o
7
6
9-77879^1
9.778960
9.779119
9-779195
9 f 017 19
9.901634
9.901539
9.901444
9.77946 3 '9-901 349
9.876063
9.876326
9.876589
.9.876851
I9.877M4
o.
o*
o.
o.
o.
13937
13674
134x14
13149
11885
41
J
1
\Qhfine \ Sm t \ ICtHtang . I Tan gent I M
Degree 53, ' 1
D egree 37.
Ml Sine | Confine \ Tangent| Co-tang. \
o
I
2
3
4
J
6
7
8
9
xo
II
12
»5
^4
15
16
20
21
22
*J
2A
3^5
9.77946519.^02549
9.779^51
^779798
9*7 7 99$ 5
9*78oi3j
9.780500
9.90^*53
9.902158
9,901065
9.901967
9.901872
9.877114] 10,12x88 5
?.877577JiP.U»6x5
9.877640
9.87790J
9.878165
9.878418
I0..X2X 3 6b
10.1x2097
10.1x1854
lIO.IXlf72
9.780467
9.7806J4
9.780968
9-781154
9.901776
9.901681
9.78080V 9.90158*5
9.901488
9901191
9.878691
9.8 7 89 5-$
9.879216
9.879478
9.879741
9.781501
9.781467
9.781654
91781800
9.781966
I0«l2Xg09
XO.XXI047
10.120784
10.IXQ$X2
XO.IXQX.59
9.90X 298
9.901202
9*90x106
9.90x010
9.900914
60
5«
5»l
51
50
9.880003I
9.880265
9.880528
9.889790
9.881052
9.782152
9.782298
9,781464
9782690
9.78179^
ko. 1x9997
X0.1197J4
IO.X 19472
10.X.X.9X10
10.1x8948
9.90O828
9«9P0722
9.900626
9^900529
9.881514
9.881576
9.881859
9.^82101
10.x 18686
10.1184x4
io.m9x6i
10.1x7899
9.782961
9.7^5 1 27
9.785191
9-783457
9.785^1^
9*900433 9'882565|ie.ii7^^y
16 9.78,5788
3 "
9*900557
9*900240
9.900144
9.900047
9.899951
9.882625
9.882886
9.885148
9.885672
49
4«
4f
44l
43
41
41
40
19
38
37l
xo. II 6066] 54
xo.11 5805 }5
10.1x5545 51
10.115281 5J
10.11 5x^x 0150
lCo->c I Sine | 1 C(>>t^/^ fJTa%nt7M
I>egree5^,
X0.1 17375
xb.xx7ii4
xo,ii685x
9.885410 10.116^90
io.ii6gx8
*9
30
9*7^l9n
9,7^4118
9.7842S2
9.7^4447
9.899854
9.899757
9.899565
9.899467
^.885954
9.884195
9-884i^57
9.884719
9*884980
Degree j ^T"
Ml Sine' I Co-Jiiu | |Tangent|. Co-tan^. |
9.78 5« J
9.78 1 S91
p.78576)
?-78j9»i
g.786088
y'784447 19-899467 1 1 9-^84^ollO'' " t<ln&|)0
9:784616
9.784776
9.78494.
9.78 lUI
928»«fw9^98j8
*-78<S(a9
9.786^4*
9^99170
9«8 99171
f.89Ji7J
9.899078
9.898 J9:
9-898494
9-7^6xit
9.7864*6 9-898»99
9.898
9-8 9(104
9.898006
9.787069
9.787*)
9.787J9J
9.787 J S7
?.7>37*o
9.^97908
9.897810
9*8971
9.897614
9-897 ^'6
9.787885 9.897418
9-897 J
9.897
9.78^045
9.78 d 10'
9.78817.
9.8971,
9- 1970.
9.788694
9.7S88J6
9.789018
9.7 8 91 So
9-789^4 :
91896916
9.896818
9.S966;
9.896»
i385»4:
.88 5,0 J
,88^761
9.386o»6
9.386x88
888177
.g836jS
.8891601
.,88941,
9.889631
,88994j
'890^04
,890461
.89071J
.890981^
891147
.89176S
S9101S
89*549
4?S8
4497
1 141 J I
I1J974
'M71
U4i
11667
11406
!n834
i,6ij
iij6:
0840
0J79
.0J18
0.1190J7
'9796
<'9iM
09*75
0875?
0849;
I Co-fJt»[ Sine ; \Co^a^. \ Tangait 1.M
DegrerjS.
111 Sine I Co-fiiit I |Tat1gcnt^C<^•ftf«^. ]
i*-» I ■ I < IBI« r I I , I I ■■ - ■ , , . '.m.
1 9*786^04
* P.7^9^^5
JJ9.7898I7
4]9^789988
5 9*79114?
(5 9*790^10
7 9.790471
8
9^9dj35 -iQ^9^njoto*r<s:d^69 51
9,8961^.^
9.8961 J7
9.8960^8
i
9.79063
9}9.79<»793
o
9.8959,9
9.895840
9^95741
9,^9041
9-79<59^4l9S9fH2
9.791596
9.79>756
9*79»i>5
9^79**75
i?i9»79«4?^
14
i6j 9,791917
179.791077
18 ^.7911^7
Jf^ 9 79*397
^^9.791557
9.89544?
9#*95HJ
9»*9f»44
9.895144
9.895045
^—»
9^9M9^* •io.idi44o9Jf7
9.895S5iiio;i6*i49f^
9.8941 iiUo.i^<889?j
iO«.iof 6iS u
*o.io^3|68 jj
i0.io^io« fi
£0^^04588*5
9.89 5 672'Klo« 1044^8 4
9.8959J2 •X0.i#d4o68 4I
9.896i9r£ li^tojSoB 4?
9.896451^ t<j>4 105548415
9.8967 i2t I6-IOI188 4f
9.^9457^
9.894^5^
9.894892
9.8951 52110.104848
9.895412
I2
14
»5
/
9*^94945
9^894846
9.894746
9.894646
9.894546
9^79x716
9 792876
9*79Jor5
9793^95
9.793 3 U
9.894446
9»<9434^
9,894246
9.894146
9.894046
i6
*7
»9
9.793 5 »3
.9.793^73
1-819.79383^
9.793991
30I9.
794149
9,893946
9.893845
9.893745
9^93^4^
9.893544
9.896971 j i(j,.iojoz8 4(
9.897231 10.1027694]
9.897491 .1^.191.50945
9.897751 19..103»249 4'
9.898oiiofi6. 101990 40
•10*10173015
i!o.i6i470 3*
tO;ioiiii 37
to. 100951 3^
to. 100692 J5
td.«oo4j2 ^4
9.898*70
9.898530
9.868789
9.899308
9.899568
9.899817
9.960086
990034^
9.900605
10,100175 II
10.09991? p
Ip 099654 ?i
io 099395 ?o
\ Confine \ Sine; | \Co^tan g. \ rangent JM
— — ^— — M^— »^»r^ j^w^— »a>— j.^» ■ 11 — - - - - -^— *
.*«4MM
Degree 51.
Degree 38.
1| Sine \ Co-fine \ )Tangent| Co-tang. \
o
X
9^94i49|9'^9?544l 19>9oo6o5|
^.794^08
^•7944^7
^.7946x^1
^.794784
^79494*
9.895444
9.895343
9.893x45
9.893141
9.893041
r
8
'2*
^79^101
9*79 1^*59
9795417
9.795575
9.79^7 33
9*900^64
9.901 XX4
9.90x383
9.90x641
9.90190 1
9.89x940
989x839
9.89x738
9..S9x'637
9.89xn^
9.90x160
9.90x419
9.96x678
9.90*937
9.903196
0,0978^9
0.097580
0.0973x1
0.09706X
ro.096803
9*795891
9.796364
9.79^5ii
9.89x435
9-891? 34
9.796206^ 9^89^x33
9,89xx3x
9.89x030
9*903455
9.903714
9.90J973
9.904x32
9*904491
^S S.79^^7^9*^9l9^9
\7 ^.79683619.89x817
V9
9'79^99^
9*797150
9.797307
9,8^17x6
9.89x614
9,891 ^xx
9^9047 50
9.905008
9,905167
9.905526
9.905784
9.797467
9.7976x1
9*797777
9.7979J4
r 5^9.798091
•^«ki*iMMW
9.89x4x7
9.89x519
9.89IXJ7
9,891 X 15
9.89101?!
9.9^^04^
91906302
^^9065 10
9.906819
9.907077
J 6 9.798147
^719.798405
J 8 9.798560
59 9-798716
<?o1 9.798872
9.8909x1 1
9.89^809
9,890707
9,890605
9*907336
9-907594
9.907851
9,908111
9 >89o5o5l !|9>^o8369J
>'099395l^o
0.0991 3 f
0.098876
0.0986x7
0.09831^8
0.098099
*9
a8
• . I
*7
261
i5
X4
*3
XX
XX
xo
0.096544
0.096185
0.0960x7
0.0957618
0.o^55O9|i5
19
18'
16
0.095x50
0.094991
0.0947 3 3
0.094474
0.0941x5
»4
^^
11
II
10
0.095955*9 ■
0.09^65^
0.093440
o.093i8x
0.0919x3
8
7
6
5
0.091664
0.091406
0.091147
0.091889
0.091631
4
3
X
I
o
ll
{Confine IPI^ine |. i£o'tarif* \ Tangent M
1 ' ■ Jiij, ■■ I • « t' ■« • I fc- < ■ ■ .. V - - '--
Deforce 3,11.
Degree 39.
■ ■« I m « - ■ I ■■ i . I
Ml Sine \C<hfine \ | Tangent J QHtang.\
1
2
3
^.79887119.89050; I ( 9*908 ? 69! 1 0.09 1 6 ^ I |6q
9.799028
9.799184
9*799U9
9*i99495
9.799651
9.890400
9.890198
9.890195
9.890093
9.8 8 9990 1
9.908617
9.908886
9.909144
9.909401
19.9056^0
10.091 37}
io«o9ti{4
10.090856
10.090598
10.090340
5^
5^
7
8
9
10
XI
XI
»3
»4
x6
17
x8
»9
»o
21
»4
16
»7
iS
19
9.799809
9.799961
9.800117
9^800171
9.800417
9.3898881
9.889785
9.889681
9.889579
9.889476
9.909918
9«9ioV6
9^9x04? 5
9.910693,
9.910951
10.090081
10.089813
10.039J65
10.089307
10.089049
9.800582
9.800737
9.800891
9.801047
9.801201
9.889374
9.889171
9.889167
9.889064
9.888961
9^911109110.088791
9.9I1467 10.088513
9.91^714 10.088175
9.911981 10.088017
1 9.91 1140 10.087760
5^
51
51
5<
—
4?
4^
4J
9.801356
9.801510
9.801665
9.801$ 19
9-80197?
9.888858
9.888755
9.888651
9.888548
9.888444
9.91 1498
9.91 1756
9.9X 3 oi 4
9.91317I
9.91 3 U9
10.^8750^
10.087144
10.086986
10.08^719
10.086471
9.801117
91802181
9.802435
9.801589
9.80174?
9;88834i
9.888237
9.88^1^3
9.888030
9.887926
9.913787
9*9 '4044
9.914302
9.9 1 45 60
9.914817
zo.o86ii3
10.085956
10.085698
10.085440
16.085183
9.801897
9.803050
9.803104
9.803357
9.80^510
Ml Sine
CO fine
9.8878111
9^8877x8
9.887614
9.8875^0
9.887406
9.91 507 f
9*9i^U^
9*9 1 5590
$^.915847
9.916104
■rf-M
10.084925
10.084668
IO.O844IO
10.084 1 5g
10.083895
4^
\Jl^tar>
9.803664
9.803817
9.80J970
9.804^25
9.80427'^
1-4
%7
^«
f4
f9
9i8oj5io^.8874o6l |9!^i6ic4| io.o8}895l3o
* Degree 3^.
M| Sine ! Co-fine \ |Tangent| Co-f^/ig. |
9.887 JOl
9.916361
9.887198
•
g.^i66i^
9,887093
9 916876
9.8879091
^.917134
9.88688<4
9.917391
10.083638
10.6^^381
10.083113
10.082866
10.082609
2-9
28
i7
26
25
9.804428
9.804K8X
9.8047 f4
9.804886
9.805038
9.886780
■9.886675
9.8^6571
9.886466
9.886361
9.917648
9.91790$
9.918 162
9>9 18420
9«9 18677
10.082352
10.0*82094
10.081837
10.081580
10.081323
2-4
22
21
10
9.805191
9.8a5343
9.805495
9.805647
9.805799
9.886257
9.886152
9,886047
9.885941
9.885837
9.918934
9.919^^9
9.919705
^.9199^1
io.o8io66
10.080809
10.018x3552
IjO;o8o295
10.080038
18
17
16I
9.805951
9.80610,3
9.806254
9.80^406
9.88573 a
9.885627
9.8855*1
9.885416
9.806557I9.885311
9.920219
9.920476
9.920733
9.920990
19.9^1147
10.07^781
10.079524
10.079267
10.079010
10.078753
12
Id
9.806709
9^806860
9.80761 1
9.8,07162
9.885205
9.885100
9.884994
9.884889
9.807314I9.884783I
9.9M 503
9.921760
9.9^2017
9.922274
9.922530
10.078496
10.078240
10.677983
io,'077726
fo.077469
I
7
61
5
9,807464
9.867615
9.807766
9.807,917
9.^84677
9.884572
9.884466
9.884360
>o 1 9.808067 19.8 8 42 5 4
9.92^87
9.913044
9,^23300
9*9i?^ 57
923813
^
10.077113
10.076956
10.076699
10.076443
10.076186
4
2
1
6
I C(hfine ™Sii)c I \C(HtaH^, | Tahgent I M
k»^
Degree 5 Oi
G
H iUi
i
\
Degree 40.
M| .Sine | Co-fine \ Tang ent { Co^tang . |
I
2
4
6
7
8
9\
lo
II
12
14
1$
9.80806719.884154! (9.9.i5*i?l
9.808118
9.808 g68
9.808519
9*^08669
9.808819
9.808969
9.809119
9.80916^
9.884148
9.884041
9.88j9j6
9.88j8i9
9.885715
9.885617
9.885510
9 882404
9.80941919.885197
9.8o9^6p
9.885 191
9.809718
9.809868
9.8 100 1 7
9.810x66
9.8105 16
9.885084
9.881977
9.88187X
9 881764
9.881657
16
iS
20
9.810465
9.810^14
9^810765
9.^8 109 II
9.^11061
II
tz
^Z
14
^l
z6
2-7
2.8
29
9.881550
9.88244^
9.8 s 25 56
9,8812:^
9.881I1I
9.8112x0
9.8II558
9.811506
9.811655
9.8 1 1804
9.88 20I 4
^.881907'
9.881799
9.881693
9881584
9.8x1952
9.8x^1100
9.812248
9.812596
9.^**144
9.881^477
9.881569
9.8812^1
9.881155
9,881045
9.924070
9-92.4?»7
9.9*4583
9.924839
9.925096
9.925551
9.92 5609 J<
9.925865
9.926121
9.926578
9.926654
9.926890
9.927147
9.927405
9.927659
9.917915
9.928171
9»928427
9.9x8683
9.928940
9.919*96
9.9^9451
9.929708.
9.929964
9.950219
9-^50475.
9.930751
9.950987
9.93 "45
9.95 1499
0.0(76186
0.07 ^9lo
0.075673
0,075417
0.075160
0.074904
0.074647
0.074391
01074135
b.073378
0,075622
0.073366
0.07^1 10
0.072853
0.072597
0.072341
60
5«
57
55
54
^3
51
51
50
0.072085
0.071329
0.071573
0.071317
0.071060
49
47
4^
4|
4^
4^1
0.070804
0.O7o54o|j-
0.070x9*13
0.070036
0.0697 8 1
0.06.9515
0*065^69
0.069013
0.068757
0.068501
« ■ III. ■ . j f ' ■ I \
' [Co-fine tSinc "f \C(P'tang.PTsin^cnt\
Degree 49.
V
Ri
Ak
Degree 4^.
Ml' Sine I Co*fvu\ 1 Taageiiq Co--tangi\
go|9.8 iiU4j9:««lb45M9.9? X4991
— — >— — ^— W^Mt^»^*1^M^— »■* III 111 ■
51
5*
33 '9*8 11988 ^.88072 X
34
51
3^
37
40
»
9.8x2691
9.812840
9.8x3135
9.8i;a85
^.880937
9;8|o8
371
£9
9»88o6fg
p.84o5o5
9.931755
^.9320fo
9.9}ii66
9-931522
9.93*778
41
42
43
44
45
13
W4
fi
9.81543b
9.81 3 $78
9^«t37*5
9i8x387x
9.8x401^
9.880397
9.88028^
9«8 80x80
9.88007x1
9.879963
9.8x4x66
^«X4ji3
9.8x44^0
9*8x4607
9*8 1:47 5 3
9.93^033
9:933289
9-^3. M45
9.9^800
^^4056
9.879855
9.879746
9.879637
#.879529
9.879410
9.«ili93
5N?m39
9ii5485|9*878875
4^
^f
4«
4^
i2
5i»»8i5777
9.8x59*3
^.8x6069
9^8x62^x5
I 1 1 1 l^M ■■
9«S L45^ol 9*87 93x1
9^34311
9^^J45^7
9.934822
9.935078
0,0667 1 i
0.66645 5
oio66to6
o.<:f65944
9.879x02
9-879099
^J7a9a4
9.878766
9»fi78656
9.87854^
9-878418
9.878318
9'93 5589
9.^35844
9*^3^355
9.936610
96 9^8x636x19.87821^1
^7 9k8x6|o6 9.878x0^
9.936866
9*937x21
9*93737^
9*S^37^3»
»a788»
58 9M66SZ
5^3^8x^797
19^8779^
9.87789<s^
^foM?4ll9«8777«<^i. 9.6j8x6j <o,p6o83'7t o
19,93814a
9.938397
9^938653
9.938908
o»6685Qrlie
o,J68^45li9
C<d67^^ 28
p.66^734 17
0,667478 26
o«66722^|^5
0.06 5 68 9
0.065433
0*665177
0.0649x2
0.064666
0*063 1 34
0.06187^
0.06261 1
0.061368
6.662x1}
i4
ii
21
20
t9
18
X7
0*6644x1 14
o,o64r'56Y3
6.663<^&]X2
0.66364.5'
).o63389
0.061858
0.061602
6.061347
IX
to
>
9
B
7
6
5
— r1
f
0.06x092 ' X
I Cff^ 1 Kne \ I Cchtam. I TangeittlM
f >
G 2
• i
Degree 4i>
Ml Sine \ Co-fine \ | Tangent I Co*-^ ^, I
o.o6o58x|59
0.0^0^X7)5^
0.060O7 2
o«o$58i6
0.0595^*
•^'
4
«
9.9 J 94ft
9*959^7 3
p.9J99i8
9.94018 J
9.9404 J 8
1^9.817088
9.81713J
9.817378
9.817515
9.817668
1
i
.4
6
7
S
9.87767O
9.877560
9.877450
9.877540
9.8771J0
9.S17815
55.817958
9.8 iS 103
91 9-^ » 8*47
10 9.818391
IX
1%
14
16
1^]
zo
^5
9.877110
9.877009
9*876899
9,876789
9.87^678
9.940695
9«940948
9-94 1 ioi
9.941458
19*941715
9.8 18 J 56
9,818681
9.818815
9.818969
9.818115
9.876568
9**7^457
9,876547
9.876156
9.876115
9.941968
9;942ii5
9.942478
9-94*7 J|
9.9419^0
1^.819^57
9.8 1 940 1
9.8x9545
1919.8x9689
9.8x9851
9.876014
9.875904
9.875795
9^875^81
9*87 5 57 1
9*943 *4g
9*945498
9*945752
9.944007
9.9440^1
9.819976
^.8zoxx9
9.810165
9.810406
9.810549
9.875459
9.875548
9.875157
9.8^75115
9.875PX.4
9*944517
|'9-94477i
9.945016
9.9:45181
#.945 5J 5
16 9.810695
9,819856 9.874791
9.?»0979
9.3iiiii
9.811164
9JK74905
9.874679 .
9,874568
9.874456
19.945790
9-94^045
■9.946299
^9^94^5 54
9.946808
0.059307
0.059051
0.058797
0*058542
0.058287
o.o59c^32
o»o57777
o«o5752i
0.0^7167
o.of7oxi
0,0567 57
OiOf^SOft
0.05^248
o.t>5599J
0.0J 57 58
Si
51
U
U
5c
5
45
0.0554^5
a*o55*%.9j5B
o*o54P:r4
0*054719
0^544^4
0.0542 zo
0,053955
O.P5570X
o.o55446r5
0.055x9% 5<
J7
5:
?3
I C0'fine I Sine j \Co^afk^. \ Tangent |J
Degree 48.
-s Degree 4?.
Mi Sine [Cthjme t' [Tangent | Co-tang. \
51
15
■»"-
H
40
41
4*
41
44
45
46
47
4»
9,8ii 1641^,8744^61 1 9«94^8o8l lo.as 3 1 92! ?o
^811407
9.811550
9.811691
9»^»»?3'5
9.8 ii 977
9.874344
#f«74ir*
9.874110
9)874668
9^873896
9*8 11 1 10
9.811161
^•811546
9.811688
9.87367%
9.947063
9-947 ri7
9.94757*
9.947816
9.94%>8i
9«Sii404 9.873560
9.873447
9.87!?? 5
9^948? 55
91948590 io.o5i^<o
9,948844
7
9^949099
9*949? 5 g
io«o5ii56
io.pr5:o^i
iOi05b64f
9.811830
9*811971 9.8731x0
9»8»JM4
9»^H391
9*873ii3
9*871998
9»8ijMf 9^87*885
9.87177*
9^941^07
9.949^^*
9.9)01 16^10.049884
9i9l^70
9I950615
9.813558
9.813680
9.813^11
49I9.81J961
50
SI
u
5J
54
55
56
57
58
59i
60
9.814x041^.871108
9.871659
9.871546
9.871434
9*87i3ii
9f95o?79
9mi^3i
9i9f«388
9*95i64»
91951:896
9.814145
9.814386
^.814517
9.814^67
9.871094
9.871981
9.87x868
9.871755
9.81480819,87x641
9«952i5o
9495*404
9\9U^S9
^9U9^3
S^9U^h
9.814949
9.815090
9.815130
9»8*5}7o
9.8i55ii
9.871518
9.87x414
9.871301
9-87 1 187
9.871073
9*9f?4*i
9-9^1^7^
9'9Uj9^9
9.9541^83
99544J7
10.051957
io.o5i61i
10.051418
10.051173
ro.ofi9i9
10.05^x6^4
xp.a5Q393
10.050x3^
10,
ibi049^75
10.049x1.1
X 0.048 8 $7
X 0.048 61 £
1 0.048 3^ a,
10.048104
10.0478^.
10.047 57 f
10.047341
10.047087
10.046833
19
18
*7j
16
14
11
11
io
18
[J7
%6
15
10.046579
10.04^31^
1 0.04607 X
ip.045817
10.045561
14
H
11
7
6
J
41
■1
1
o'
I Co^m I Sine | {Co-ta^. [ TanggntI M
N.
Degree 4^*
ML Sine I Oo^fine^ V \ll^r\&^t\ Co-tang.
*_ I < III I . 11
o
%
I
4
7
14
»4
&5
$i!i^6^it^ 9A$99n
9,«a55iM9^87lo7?l l9»9H4?7lio*04ll4i
^ " _! .^ -- - -
9.8(x6^i I
9^.870*04
9f^$469iLi(\o4t$oa
9t^J494»a^«04tcif4
9tf55x99
9t95Uf^
1 0(9441 00
10^04454^
9t951f^Tro»P44»92
jJ(»j5(?5i
^•aa54^i ^87^171
9»8it7.$»8.
9>8474^7
9*8 703 90
9^8.704^9
91870047
^5^94f4
9v9fT*n
9^9^7485
9i9577?9
9^9^7995
9i9f*»4^
iD«94X7tf
aGb^4&5>l
lQ»04^f€i
ip^P4^oof
ic^Q4tyy^
____ ^1
9»97(9^||io«o44o^a
9^90»«^ «0^«>4?7t4j5?
9!»9ilM^»a*04Jt3ij5a
9*9$^7^^ (ia*94$276j
9*956977 a 0.04^0 a 3
fi
t"8 17745
8!&7884
:.8i8pft}
'o,^|b8i6i
^Si8;ot
9,86j)ft4f
9«S$9i}Q
9;i69ott
9*868949
9*8^i7l$
^958fQo
9^95^7 14
94919008;
9^9$9x6ti .|[o*O407}ft 4,1
9;9t9tx5
|9.8^8459|9.a686tQ
918287 »6:
p.8a899^
9,86»4JS^
^8^895*9.8685^4
9»868sd9
9:9197^9
9(9600^^
9^60177
9»9^<s»5 JO
9J960784
{|^ 9*819 1^119.86^09$
9*8 19169 9«84797^
^829407 9.86786%
^81.95419*^^747
9*8 1968 ;( 9*8676 ;(x
|p«04K 500
40*041246
«0kO4Q99ft4
^6;>04^8 5
J^
^■■'t
9*9610^8
9*96si9K
9^9^x14*
9,96x799
9*961052
90^040 iji
lo«oj^977-
fo,ot97ij' ^
90,019469^^
so.or$5^fti^a5
!J0*Ojt^9^»
1o,4j845i-
to*(i$8iOf^
^?tOiz^47ljg
Ci^Jine 1* Sine [ 1Cb-f4Vf/;*jT«Sit
De^c 47.
Mii
,>
JI 9.!^s8lI
9.8671,!
9.961J06
0.0 J 7694 iS
33 9.8joosi»
9.867599
9.961,60
O.OJ7440 18
9.867183
9.9618 ,3
0.057187 17
34 9.8i»i34
9.867167
9.963067
o.oj6j}} 16
35 9.S!o!7i
9.867a!'
9.963310
o.Qi66So »5
3< 9.8^0509
9.86693!,
9.96!!7, ,0.0564.6 14
37 9,830646
9.8 668,91
9.963817 ,0.056175 13
38 9.830784
9.S66703
9.964081 io.o5!9,9 1*
39 9.830911
9.866336
9.^6435, ,o.o3!66! 11
,o9.8!io!«
9.866,70
9.96,!88 ,0.93 !4i« 10
19.83,19!
9.866;!!
9.9648,1 ,o.o;!,!8 ,s
. 9.85,331
9.866,!7
9.96,09! 10.05490, 1
3 9.83,469
9.866110
9.9'fS!48
10.034651 I
,9.83,606
9.866oon
9.961601
io.o!4jSt8 1
.5 9.83,741
9.S6!88,
9.56iS!i
io.cj4f44 '
,6 9.8SI»79
9.86!77o
9.966-109
io.ojj89< I
47 9.8310,1
9,860!J
9.966561
io.ojjej8 1
t! 9.'!""ti
9.86si!6
j.,66616
10.0! J J 84 I
49 9;Sjii»8
9.86,4,9
9.966869
lO-PiJIJl I
!o 9.83141!
9.86!5o«
9.9«7iii
JI 9.83156, 9.863,8!
9967J76
iooj76r4"
!i 9.8!.«97 9.86I06I
9.967619
10.0J1J71
53 9.8318^3 9.8649!o
9.967885
10.031117
!4 9.831965^9.864833
9.968156
10.0J1S64
!! 9.831,0! 9.B64716 19.968389
'o.oi'6ii _
!6 983314, 9.864!9a
9.96864
10.0JI357
!, 9.8JJ376 9.864480
9.968896
IO.0JIIO4
U 9.83!!, 1 9,8 64!«S
9.9691,
10.0308 Si
!9 9.833648 9.86414!
609.833783 9.864,17
9.96940
lOrfSIOJpT
9.9696,61 io.o^o!44|
_0
\Ctfnt' Sine 1 iCa-lma. \Tat^nt \
Degree 47.
G +
V
Ml Sine | Ci>Jbte \ lTangent| Co^tat^,]
Degree 43.
■ I— ^^t^— K* ■ ■ ■ ■ ■ ■ — 11 ■ —
3
4
5
9-8 3 4 591
7 9?8H73o
8 9.834865
9 9.834995>
9.8351U
7
8
21
12
^4
9.853919
9*834054
9.834189
9.^343*4
9.834460
9.86401 o
9.863892
9.863774
9.863656
9.86353^
9.969909
9,970 1 6i
9.970416
9.970669
9.970922
9.863419
9.863361
9.863183
9..863064
9.8629^
9-971175
9.97 1428
9.971682
^.972188
9.835x69
9.835503
9.835538
9.835672
9.83 5806
9.86x827
9.862709
9.862590
9,862471
9.862353
9.972441
9^971694
9,972948
9.^73*011
9.973454'
.9.835941
9.836075
9.836209
9.836343
9.83^477
jfe862234
9-^115
9,8?%^,
9.861877
9.861757
9,8 J 66 II
9.836745
9.836878
9.837011
98^7146
2.<
28
29
3^
■*^^-««"ii."
'9.861638
9.861519
9-86i'399
9.861280
9.8611^1
9*973707
9.973960
.9.974213
9.^74466
0jig747i9
9.^37179
9.8 374 1 i
9.837546
9.837679
^^8378 1 1
9-974973
9.9751^9
9:97 5479
9.97 57 31
g>975985
9.861041
9.660921
^.8 608b 1
9.860681
9.860562
' h.v
9.97<'238
9.976491
9.976744
9-97^997
9.977250
0.030051
0.029S38
0.02^584
0.0^933
0^02*9078
5!
|5i
51
50
0.028827
0,028571
.0.0x8318
0.02.8065
0.0278 12
o.027 5 59|4j
0,027306(41
0.027052 4?
0.0267994^
44
4J
4i
4J
401
0.026546
0^026192
0.02^040
0.0*25787
0.02 5 5«
0.025^50
0.025027 J9
0.024521 37
0.024x6! 36
0.02 4015 3^
34
3J
3>
3
3o|
0.023761
0.623509
0.023256
0.02 J 09 3
0.022750
■ ■. . 1 ■ »• ' ' ■■ II I.I »- ■ , I , - ' .
\Cv'fwt I Sine | \Co-tang. | Tangent |M
ee;rec 46.
4*
J
' 1
f
\
• •»
,">.
> t
•■..<
A
;
TAB L E
OF
Logarithm Numbers,
From One to Ten thousand ;
WHEREBY
The Logarithm of Any Numbef
under 400CXX) may be rcadfly
difcovered.
%,^— *— i— **»»ii*>»«—i^*— *— ■ > ' . •' ""
' ' 1.
4»
LONDON,
Printed by K Clark, Anna DQm<
MDCLXXVin.
9 •
>v
Nl Leg. I iNl Lqg, I jNl LoiTT^
4
5
o*oooo«o
0.301030
0.477 121
0.^02060
0.698970
6I0.77S15I
34
?7
39
1.544068
1.55630$
1.^8202
67
68
69
70
172
i.«z6o75
1.831509^
1.838849^
1,845098;
1.851155
1.85735*'
•«>4b
0.8450981
0.90 5 090^
0.954*42.
1. 000000
X1I1.041393
iz|i.©79i8i
7
8
lo
40 i.6o2o6o
41 1.61Z784
42 1.6 £3 249
43 1.633468
44I1.643452
l45'i.653iia|
73
74
75
76
77
(78
1*863 3 fc|-
1.86913 ft
1.875061
1.8 808 1 5
1.886491
1.892094
1311.1^943
1.146128'
1.176091
1.204120
1.230449
.2552721
46
47
48
49
50
51
1.6627581
1.672098
1.681241
.690196
698970
1.707 $70!
I
79
80
81
82
83
84
— — T
J.897627
1.903090
1.908485
1.913814
1.919078
1.924279
1.278753
I.3OIO3O
I«322219
1.342422
23I1. 361728
24ii.38p2H
52
u
54
55
56
157
1.7160031
1.7*4276
i'.73*J94
1.740362
1.748 188
i.755^75j
85 1.929419
36 1*934498
87 ^*939i^9
83 1.944482
89 *.94939^
l9oli.9l42'42
25
26
*7
28
*9
30
X.597940
1.414973
1*43*3^4
^•447158
1*462398
1.477 121
15811.763428
'59I1.770852I
60 1.778151
61 I.785330
62 1.792391
63 1.799340I
91
9*
93
94
95
1 96
1.959041
1.963788
1.9684S3
1.97 3 "8
1.9777^-3
i;98227i
-.*-*-
31I1.491361
32U.505150
3311.518514
j64|t.8o6i8ol
|65|i.8ii9i3i
I66IX.819544I
97
t.98677fc
1.99 122^
99ii99illl
Nil O I I I 3 I 3 I
Tbk Table af Logarithmesi
-*■
oo
oooooo
OI
004^11
01
008600
01
012857
04
017055
000454
004751
009026
015259
017451
000868
005181
009451
015679
017898
05
06
07
08
09
021189
025506
029584
053424
057426
021605
0257M
029789
055826
037825
022016
0261 25
030195
0J4227
058225
001501
005609
009876
014100
018284
— --^
001754
00^038
010x99
o
01
i45ii(
18700I
0224x8
026535
O5059P
034628
058620
022,^41
026942
031004
03^029}
059^171
10
II
12
»J
14
041395
04531?
049218
055078
056905
041787
045714
049606
055465
057286
642182
046105
049995
05584^
057666
042576
04^4^5
050579
054229
058046
04^969
0.46885
050765
054^'^
058426
X5
16
17
i8
»9
060698
064458
06.8 186
071882
07-5547
061075
064852
068557
072249
075912
061452
065206
068928
0716x7
076276
061829
065579
069298
072985
076640
062106
065953
069668
073^55*
077004
20
21
22
»4
079181
082785
086559
089905
095422
07954J
085x44
086716
090258
095772
079904
085505
087071
090610
094122
080266
085861
087426
090965
094471
080626
^842x9
08^781
091315
09.4'8 20
15
26
»7
28
^9
096910
100371
105804
X07209
X00589
097257
100715
104146
107549
100926
097604
101059
X04487
10788^
I II 265
097951
ioi40|
X 048 28
108227
IXI599
098298
101747
105169
J108565)
yi9j4
The Table of Logarithms.
$ I 6 I 7 I 8 I 9 llD
006466
bl<3jr2,4
014940
OI9I16
■
027549
051408
ibg54i9
1039414
■^«>
001598
066894
011I47
015559
019531
0030x9
007321
011570
015779
I019947
003461
0077^8
011995
016197
020361
003891
008174
ot24i5
016616
020775I
45*
428
414
419
416
023664
017757
031811
03582-9
039811
024075
028164
032216
036229
040207
024486
028571
051619
036619
040602
614896
018978
033011
037^:^18
040998
411
408
404
400!
^g6
0435^1
047175
051153
054^96
058805
045755
047664
051558
j05f578
lo59t
35
544148
048055
051914
055760
I059565
044539
048442
052509
056142
05994s
0449 5 i
o4B'83o
©52694
056524
060520
i9i
?79i
061581
066116
I070038'
075718
1077568
080987
[084576
)88i56
P91667
^95169
062958
o666p^
070407
074085
077751
0^3555
067071
070776
074451
078094
063769
067443
07it45
05^4816
078457
06408 3 j
067^15
671514
075182
078819
57^
572-
5<59.
366'
5^5
081347
084934
088490
092018
095518
081707
085191
088845
092369
0958616
082067^
085647
089198
091721
096215
082416
086004
089552
0^5671
096561
^98 644*098989
P02091
105510
1108963
101434
105851
099355
101777
106191
169141 10^579
iiii6(^ 112605I111959
0^9681
103119
|io65}i
109916
Ii3i7_5
H
10662^
1034^1
106871
.110153
111 5^991
360;
5 57i
M5i
351!
54^.
346
543
546
558;
!ZT&# TahU of Logarithms.
N II o I 1 I Of I . 3 I' 4
mI
110^74
117105
1141771^14611
ii76ogni79^34
11090^1111131
114178T1 14504
i I 4944
118165
111559
114830
118076
11J178
1185^5
X11M8
1x5156
«35
139
JI30334
133539
136711
139879
143015
1 3065 f
133858
X37037
140194
»30977ji3"98
i34»77 13449^
»37354
140508
i433i7U43^39
137^71
1408 IX
114^951
1 3 1619
IJ48M
^179H
141134
11441^3
141
141
»43
:t44
146118
149119
151188
146438
1495x7
I152.594
»5533^P55^39
Ii5836ih58664
1467481147658114,7367
149835 150141 150449
151899 153x05 »535o9
« 55943 156146 156549
158965I159X66I159567
H5
146
M7
M8
161368
1^43^53
1X67317
161667
164650
16761}
1701611170555
M9|lx73 1^^1*73478
161967
i<'54947
167908
170848
173769
1611661x61564
1651441165541
1 68 103 1 1 68 497
17114XJ171434
"74059U74351
i5olfi76o9iti7638i
151
151
153
154
,178977
181844
I 8469 I
179164
1^1119
184975
176669
17955X
r8i4i5
185159
176959
179839
181699
x8554x
i875iifi87»05|i88o84|i8a3i6
»77»4<,
iSbii6l
1-8x9851
18581
1^864:
155
156
X57
158
159
1903*31
193115
195899
198657
xo'397
i9o6j2r|'i9o89iVi5ii7 1
1934031193^81
196176 196453
198932 199106
ioi67olioi943
»ayb
^93959
196719
199481
101116
l*iM
I9I45I
i94aJ7
197005
'^9755
X01488
— >?i
The TMe 0/ Logarithms.
J I tf I 7 I 8 I 9 ||D
\%xx\6 121544
^^$4|^i 12^806
(2.87x21129045
'4M49
'44574
132259
i}86i8
14176J
144885
147^75
15075^
155815
147^5
1510^3
M4II9
M7M4
598i^8) 160168
i6286)U^3i6i|
165838 166134
168792 169086
171726 172019
»74<54« "7495*
17753^
180413
183269
186^08
188^28
177825
180^99
186391
189209
T91730
^94^4
197^81
19x069
^9479*
19755^
2. 000291200303
*',0i76i|iotO33.
16276
19586
22871
26131
29368
?*579
M7^9
38954
42076
451:9^
481941
513^59
544*3
57457
60469
^M59
66450
69380
71311
75%xi
781131
80986
8J839
86674
89490
922891
95069
97831
00577
16608
199M
23198
26456
29689
116939
120245
tiS5i5
126781
130012
m
no
328
315
51J
32899
36086
J9149
42389
45507
«3J*i9
136405
139564
142702
145818
48603
51676
547 1«
57759
60769
14891I
151982
155:^31
1 58061
161068
3'T
3M
3U
3^9
307
305
303
301
63758
66726
69674
72603
755«i
78401
81272
8412J
86956
89771
164055
167022
172895
175802
178689
181558
184407
187239
190051
^99
297
195
193
291
289
187
285
185
181
92567
95346
9^107
00850
3 577
19^846
195623
198382
2011x4
103848
H a
U79
278
276
174
s. 17^
Nil
,. . ... I I . ■
The Tfhfe of Logarithm^.
^m^m.
I I I. 2 I 3 I. 4
x6o
i6i
163
164
204II9
206816
109515
211187
114844
104391
107090
109783
111454
104663
107365
11005 I
111710
II5IO9I115375
»o49J4
207364
1103x9
111986
205x04
207904
210586
213251
115^381215501
165
166
167
168
169
117484
110108
111716
115309
117887
117747
110365
111976
1*5568
118x41
1180IQ
110631
113136
115817
118400
817*;
H8173
210891
111496
116084
1186J7
21S536
221153
iiJ755
226341
228913
J70
130449
130704
130959
1311x5
171
131996
1133150
133504
i337?7
171
1355*8
135781
136033
136185
»73
138046
1^8197
138548
138799
»74
140549
[140799
141048
141197
131460
134011
*3<^537
139049
141546
»75
143038
143186
143*34
143781
X76
145515
1457^9
146006
146151
177
1479'W
148119
148464
148709
178
150410
150664'
150908
i5ii5i
179
151853
15J096
153334
155580
244029
246499
24?954
151395
253812
180
181
i8i
183
184
185
186
187
188
189
155173^155514
157679
160071
161451
157918
160309
161688
1648181165054
155 99^
158398
16078^7
263161
1^5515
256x37
258637
261025
263 39^
265761
I
j
167171
169513
171841
174158
176461
167406
169746
171074
174389
176^91
16764!
169979
171306
174619
176911
167875
170113
171538
174850
177^51
268 iq
17044
27276
175081
i77?79 t
TheTablecfLegaritbms. j
5 . i tf ( 7 I S "^ 9 Iid|
10S47S
105746
io6oi6|io6»86iio65f6
171
Z08173
108441
1087 'c
108978 109147
169
X1085J
iiilii
11.388
111654 11191.
167
»ijTi8
113783
114049
114314114579
166
^16166
1164.^
11669^
116957 117111
164
118798
119060
119513
119585
1.9846
161
XII4I4
11.675
111936
111.96
111456
161
114015
114174
114UJ
114791
iiSoJi
159
iitflp?
116858
11711I
ii.jei
117619
158
1JI714
1194*6
119681
119938
130I93
M6
131979 »3"J4
13148B
iji74i|
M4
134164
134517
1J4770
135013
135176
151
156789
137041
137191
137544
i?7795^
151
135199
1J9549
139799
140049
140199:
150
»4'79i
141044
141193 14154'
1417B9
14s
14*177
144515
144771 145019
145166
148
i^S/*!
146991
147137
147481
1,7718
i4<
Miijs
14944J
149*87
149931
150176
145
151658
15188,
151115
151368
151610
143
154064 *Uio6
154548
154789 liJoj't
141
156477
1I6718
15695*
1J7198
15743?
141
15*877
1I9116
150355
159594
159833
iJS
i6u6l
161501
16.739
161976
1611,4
158
163636
i6j87j
164109
164346
164581
1J7
165S96
166131
r66467U667otti669J7
1J5
168544168578
iSaSii 169046 169179
134
no6T9 170911
i7"^"44 171J77 171609
113
ni7J»JJ
1754^4 17^696 17J917
131
u 175541.
175771 176001 176131
ijo
0?W7«J8
178067 I7B196 17851?
Tbt TkMe ef Logatithmt,
Nil o I I I 3 I 3 I 4
■»-«
m^
191
191
n8754
1810} 5
185557
87891
178^81
281161
185527
285782
2880x6
27911 iU79459l27^«y
181488
286007
288^249
28l7i4liti94i
2^«5979M4xo5
2862321286456
28847 $1288696
^9i
196
197
198
199
290035
t9ii56
294466
f«85j
20a
201
20
20
104
1
206
tQ7
208
209
ISO
211
111
2X3
Hi
115
216
217J
hi8
21
li2
190157
291478
194687
19^884
199071
190479
291699
294907
197104
1^9189
190791
192920
295127
*^7?i3
199507
290925
293X41
*95347
*9754i
^997 25
01019
03190
05351
07496
09630
301247
J03412
3o5;5^6
307^709
309841
«i754
13867
15970
1B063
10x46
311966
314078
316180
318272
J10354
* m
X1119
14181
1.6336
18379
311416
314488
3»^54x
318583
3o4i4h3o6i7
Hi
314J8
34454
3^459
38456
40444
331640
334^55
336659
338656
31^0642
01464
03618
05781
07924
10656
XI 177
14189
16389
18481
10561
12633
24694
16745
28787
30819
31841
34856
368 59l
38^56
540841
01681
03844
105996
08137
10168
301898
304055
306111
308351
310481
11389
14499
16599
18689
10769
3 1 x6co
3 14709
316809
318898
310977
11839
14899
16949
18991
31011
3*3046
5»5io5
317155
3*9194
351115
35044
35057I
37059
39054
410^9
3^^*4^
3l5af7
337*591
339*53
54i*J7l
The T»ble of Logarithm^.
5 I .6 1 7 I 8 I 9- HD
■Ms*"
279^91
281169
a844li
186681
188919118914}
18012}
28 1596;
18465^6
186905
19x147
1953^*
19556*7
197761
»9994«
1913^9
195787
197979
}ooi6i
i8o}5i
181611
184881
287 1 19
189^66
19159"
195804
i96cf07
A98X98
500378
180578
181849
185107
187354
189589
180806
185075
285331
187578
289811
19181}
194025
296216
298416
30059^
292034
294246
296446
298635
300*13
218
227
226
225
223
111
21I
120
i»9
218I
301114
304*7$
306415
?o856^h
31069J
3013 3 >
304491
506639
308778
310906
30*547
304706
306854
508991
3 1 X X 18
301764
3049* »'
507068.
309104
|3"5*9
502979
30^436
307281
309417
31154M
117
1x6
115
21,
211
312811
5149*0
517018
[319106
321184
13023:
15130
5«:3*34
315340
3^743^
2
i$3H 3195*
1139JJ31C598
J 13445
315551
517646
319750
511805
315656
^15760
3*7854
519938
51101*1^207
2ii
210
209
208
n*i
3*3*5*
5*53«o
3*7359
329598
|3JHi7
3
3
3
3
1J458
*55i^
17565
*96oi
31629
3136651313871
315711 515916
517767 51797*
519805
331851
330008
3*4077
316151
318176
350111
33*034133**36
106
105
104
103
101
13334471353^49
mi458h35<^.58
B37459
339451
IhM35
337^59
5596^50
533850I334051
335859
337859
539849
j4i6?*ri^i83o
336059
338058
340047
34*oi8
lU
334*53
556159
338*57
540146
34***5
101
261
zoo
199
198
i
T^^^
■ » ' ■ ■ - - ' I -^"
I Thf Table of Logarithms.
N II o I r I a I 3 1 4
no
^24
'1
2Z7
1X9
230
232
134
t?5
236
23»
239
240
241
242
.H4
246
^47
248
249
^.1728
i6^^I2
365488
67356
69216
42422^
44J9i
4^3f3
48305
50248
52183
J4109
56026
5i>835
71068
72912
74748
76577
.7839S
8C2II
82017
83815
85666
87389
89166
90955
92607
9.4452i
96199
42^20
445*9
46549
48499
50442
5*375
54301
56217
581*5
60025
61917
63799
65675
67 541
69401
71*53
7 J 096
74932.
76759
7857^
80391
82197
? 399.5
65^85
87568I
42817
447*5
46744
48694
50636
J43014
344981
346939
348839
350829
343iii
34517S
34^135
349033
35,1023
52568
$4493
5640?
58316
60315
351761195x954
3546851354876
35659913*56790
3585061358696
360404I360593
I**!
62105
63988
65862
67729
69587
71437
73179
75115
76942
78761
362294
364176
J 66049
367915
369772
371622
373464
375^98
377IZ4
378943
80573
82377
94»74
85964
87746
380754
382557
3?4?53
386142
387913
36*481
364363
366236
368x01
369958
371806
373647
375481
377306
3791*4
3809^4
38*737
384553
386321
388101
895520
9^288
93048
94802
96548
389698
39x464
393114
394977
396711
389875
39i64i[
13933:
395x511
■7^
■]
■^fr-'-r,*^'!—
^ TheTabk ofLogarithms^.
5 \ 6 I 7 1 8 I 9
1543 409
|?45373
347330
3492'78
[353147
1355068
356981
U^8S86
I366783
1362671
(?6455i
1 3 6642.3
368287
370143
371991
3738JI
37566^
377485
379306
?8iii5
382917
384712
586499
388279
390051I
391817
393575
395316
1^707 1
43606
45 5^9
47515
4947*
51409
53339
55139
57171
*59b76
60972
628^9
^47 39
66609
68473
70328
72-1 7 5
74015
75846
77670.
79487
81296
83097
84891
86677
88456
90228
91993
93*751
95501
97145
43802
45766
4773-04347915
49659
5160J
53531
55451
573^^3
59266
61161
343999
34596.1
349860
351796
353714
355^^43
357554
359456
361350
344196
346157
3481 10
350054
351989
353916
355834
357744
359646
J61539
6^3048
64926
667^6
68659
70513
71359
74 1 98
76029
77852
79668
^6^1 16
3651 1 3
366983
368845
370698
363424
365301
367169
369030
370882
371544(371718
374381
376212
378034
379849
374565
37^394
578216
380030
-U.a
81476
83277
85069
8^856
88634
381656
383456
385149
387034
388811
381837
383636
385428
387212
388989
90405
9.2 1 6^
93916
95676
97419
390582
391345
394101
39585b
397591
390759
392511
394177
396025
397766
D
97'
^6
str
94
93
9i
91;
9i|
90
88.
88j
87;
86i
85
84
84!
83
82
81
Vi
3o
79
78
78
77
76
76J
n\
74!
I The Table of Logarithms.
N II o 1 I I 2 I 3 I 4
%%0
i5i
X54
597940
599674
40x401
405 III
404854
598114
40157J
403192
5981871598461
400019
401745
405464
4050051405^76
400191
401917
405655
405546
400^65
40x089
^0^807
405517
x55
15^
>57
Z58
*.J9
4065401406710140688 11407051
408159I408409I408579 408749
409955 Uioioi
411619I4I1788
413*994154^7
410171
411956
415655
410439
4X1M4
413803
4072.11
40891s
410609
411x95
413909
160
x$z
165
164
414975
416641
4I850I
419956
411604
415140
416807
418467
410111
41x768
415507
4x6973
418655
410189
4*1955
4* 5474
4171J9
418798
41045 1
412097
415^41
417506
418964
410616
41x261
>«**«■
*65l
166
167
x68
169
^79
17I
171
*75
174
415146
414881
416511
418135
4*975*
45 1 564
431969
454569
436J65
437751
4*5409
4*5645
416674
4*8197
4*9914
4*5574
415108
416856
418459
45007 5
4*5757
4*5571
416999
418611
450156
4*5poi
4*5554i
417 t6i
418785
450598
4515*5
4531*9
4547*9
45^3**
457909
451685
435x89
454888
436481
458967
451846
435449
43 5048
436659
458116
45x007
455609
455*07
456799
45«3M
*75
X76
1*77
178
1*79
459333
440909
441479
444045
445604
459491I439648
441066
44*657
444^01
445759
4598061439964
441581 441538
^^-.^, 441949J44J106
444357 444513I444669J
44591 5I44607J l446xx.^
441**4
44*795
— ' . ' . ■ ■ '■ ■ i ■ ■■■
The Table of Logarithms.
•*Wi
5 1 6 1 7 I 8 4 9- IID
^98808
400558 400^11
4Qxz6i
405978
405688
J9898 I
402435
404149
405858
400885
401605
404520
40602^
599528
401056
402777
40449*
406199
599501
401228
401949
404665
406569
407591
409087
410777
4x2461
4x4157
407561
407751
407901
408 070 j
4<^9*57
409426
409595
409764
410946
411114
41128J
41145*
41 2629
41279^
412964
41515*
4II4Q5
41447*
414659
414806
415808
41747*
419129
420781
4l59:f4
417658
41^295
420945
4224261412589
416141
417804
419460
421110
14**754
416508
417969
419625
421275
422918
416474
418155
4x9791
4*i4?9
425082
•VMlB
14240651414148
4*5^97
14*73*4
14*8944
I450559
425860
427486
429106
430719
4*439*
426025
427648
419^68
43o?.8i
4*4555
426186
42781 1
429429
1451042
4*4718
426549
4*7973
4*9591
451*05
1432167143^528
143^769
4353^6
4369^7
43854*
4339*9
435526
457^^16
438701
432488
454089
455685
437*75
438859
432649
434249
435844
1437433
I439175
432809
434469
456004
43759*
4391^5
440122
441695
445*63
4448*5
440279
441852
443419
44498 1
446382I446557
440437
442009
445576
445137
446692
440<94J
442166
44373*
445*93
446848
44CX75*
44*5*3
445889
445449
44:10051
irtkiiU
11
7J
7*
71
71
70
69
69
6%
61
64
6i
6i
6 1
6t
60
^9
J8
J7
57
li
The Table of Logarithms.
N II o '^ f 1^ 3 I 3^ I 4
-^-ta
281
28]
284
447158
44870^
452049
45178^
45^18
447^1?
448861
450405
45I9J9
45H71
447468
449015
450H7
452093
45j6i4
447^>3
449169
45071'!
452247
453777
44777^
449^24
450865I
4525991
285
286
287
2,88
289
454845
456566
457889
45959*
460898
454997
456518
458053
45954^
461048
455149
456669
458184
459^94
461 198
455302
456821
458336
459845
461348
290
291
292
2.93
294
4^2398
463 893
4^5383
466868
468347
461548
464042
4^553*
467016
468495
461647
46419 X
465680
467164
468643
;t95
296
298
299
469822
47l»9»
472756
474216
47 5^7 »
469969
471438
472903
4745^1
47T816
470116
471585
473049
474508
4759^*
462847
494HO
465829
467312'
468790
47?>2'^3
471752
473195
474^53
476107
455454
45^975
458487
^5999S\
461499
462997
464489
465977
467460
468938
470410
471878
473341
474799
f 76251
300
301
302
?o3
304
4771*1
478566
480007
481443
482874
477266
4787*1
480151
481586
483016
47741 X
478855
480294
481729
483159
477555 477^99
478999
480438
481872
483302
?o5
306
307
308
109
484299
485721
487138
488551
48^58
484442 484585
485863
487*79
488692
490099
486005
487421
488333
490239
484727
486147
4875^3
488974
496379
479H3
480582
482016
483445!
484869
486289
487704
489114/
490516
The Table of Logarithms.
5 I 6 I 7 I S I 9 II D
K7P?i 448088
^49478 449633
[.51018 451172
1-5^553 4^*7©^
^5[4o8^
^55606]
H7i*5
^58638
4.60146
461649
448241
4497^7
4^(131^
4^1859
454155 4S4387
4557581455910
457418
4589J9
460447
448397
449941
451479
453011
454539I
448552
450095
4516J3
45J165
454692
155
154
154
45717^
458789
460296
461799
456062
457579
459091
460597
456214
457731
45914a
460748
461948 462098I462248
152
Ml
151
150
463146
464639
466126
467608
469085
463296
4^4788
466274
467756
4^9233
4^3445
464936
4^(542 3
4^3594
465085
466571
467904 4^8052
469380 469527
4^3744
465234
466719
468199
469675
4705571470704
472025 472171
473487
474944
476397
473633
475089
476542
470851
4723^8
473779
475235
476687'
470998
472464
473925
475381
479832
471145
472610
474071
475526
476976
477844I477989
479287
4S0725
482159
483587
«^1^^^B»* ■'■■
485011
4S64 3
487845
M9255
479431
480869
4?2302^
483729
478133I478278
479575
481012
482445
483872
479719
481156
482588
484015
478422
479863
481299
482731
484157
150
H9
149
148
147
147
146
X46
146
145
145
144
144
143
143
48515^
486572
4879S6
, . .. 489396
I490661I490801
485295 485437I485579
486714 48685514869971
488127 488269I488409
489537 4896771489818
490 94114910811491221
142
142
141
141
r\
The Tdble of Log»itbms.
Nil o I I I 3 I 3 I 4
Jioj
J"
P4
49156*
49*7^
494M5
49^^44
49^9*9
49i5o*l49i^4i|49i7SH 4919^2
491900
494*94
4956S5
497068
4^505* 495 »79l49J?i!
4944J 5l494$7* 4947X 'I
4958ii|49596ol496o9i
497»o6|497 }44l4974g3J
498?li|498448
4998x4
501196
498(86
499961
501041501700
^03917150406^
4987MI
500099
501470
501857
4988^1
500x3
501607
50197 J
504199 504355
505186
506640
507991
509^7
510679
5o54»»Wo5557
506776I506911
5o8ii6|5o8i6o
5094711509606
5io8i'5;fi0947
511C17
514681
516006
511x51
513484
5»6i39
512184
5136x7
51481^514946
|5I7»9^ 5173*8*517459
• ■■«'!■ ■ m ■■■ "' ■ ■ ■-
5186461518777
5X6171
5X759*
5O5693J
5070461
508395
509740
5X1081
5xi4it
5x3750
5x5079
516403
5177M
rf5i4
19818
11x38
11444
13746
511169
5>^575
5*3«7^
510090
511399
511705
5 14006
5x8909
5ioiii
511530
511835
514x36
5x9040
5io353{
5x2^66
514166
516469
5*7759
519045
>530Ji?
515304
516598
'517888
519174
530456
5*5434
516717
518016
519301
530584
515563
516856
518145
519430
5307?a j
The Table tf Logarithms.
5 \. 6 \ 7 I 8 I 9 11 D
4920^2/49x101
493458I493597
4948 50
496238
4979*1
494989
496376
14^7759
4937 ?7
495128
49^5,1 5
497897
492481
493876
495267
498035
492611
494015
495406
496791
498173
140
»38
,98999
iSpo374
501744
15 Q? 109
1504471
•mm
495157
500510
501880
503246
^04607
499^^7 5l4994»*
500648
5020I7
503382I
504745
500785
502^54
503518
504878
499549
500922
502291
503655
^05014
138
137
M7
136
136
505828
507 18 1-
508529
509894
511215
5p59<54l5o6o99l5o6234|5o6369
5075 »6f 507451
I08664 508799
510009 510I43
151154915x1
507586
508934
^10277
507721
509068
510411
511616 511749
-
5u55'i
513883
515211
16535
7855
51
5 12684
514016
515544
516668
517987
512818
514149
515476
516796
51SX19
512951
514282
515609
516952
518251
5x5084
5144*^5
515741
517064
5x8381
136
»5<
«55
134
154
^55
»55
15*
132
5x9171
•{510484
5x1791
523096
524396
5x9505
520615
521922
523226
524526
5x9454
f20745
522053
525^56
524656
519566
52C876
^2218 3
523486
5*4785
5196971
5^ioof
522514
523616
5249x5
X5X
131
X5X
150
11x50
515693
526^85
528174
525822
5271.14
528402
iiS 55,9 529687
52595x1526081
527243 527372
5285311^28659
-529815
??o859|55o968|5?xoj>6
519945
52^210
527501
5^^8788
550072
1129
129
129
X28
53X35xl|si8
The Table of Logarithms.
\
Nil
o
I 2 I 3 I 4
540
Hi
54^
345
546
347
348
349
J JO
364
?^7
368
j6p
5»479
3*754
34016
55194
3^558
57819
39076
40319
4^579
41825
5 3 1^07
531881
5HI5J
5354*1
536685
5P734I531862
533^09
5 i 4*80
535547
536811
53^937
533»3^
554407
535674 535«oo
537063
537945
53910X
540455
541704
541949
538071
539517
540579
541819
545074
5j8i97
55945*
540705
541955
5583*^
559578
54^819
54x078
543 1991543 51-3
44008
45507
46545
47775
49003
544X'9i
545451
546666
547898
549116
5445»^
545555
546789
548011
549M9
54444<*
545678
54^913
548x44
54957 »
544564
5458oi
547036
548*67
549494
50118
51449
51668
53885
55094
5503-51
551571
551789
5 5.4004
55fii5
550473
551694
5519"
554116
555356
550595
551816
553055
554457
1554147
5to7i7
55x938
553155
554568
555578
563^3
57057
58709
59907
61101
556415
557617
558819
560016
561111
5565441556664
557748
558948
560146
56135^
.556785
557988
559x88
560385
5578^68
559068
560165 , _^^
5614591561578
61193
95481
6^666
65S48
67016
561411
565599
564784
567144
561531
561649
.563718
565837
564903
565021
566084
566102
567162
•567379
561769
565955
565139
566319
56749/!
Ti^^ ri^& of Logarithms.
«N»i
5 1 '6 1:7 I 8 I 9 II
J 34661
J559»7
J 57 18^
158448
^59703
S409S$
54*2.03
54H47
544^88
545.9*5
547 » 59
1548389
549616
5g2M5
535518
554787
5560I5
557515
55x37*
555645
5349*4
556179
557441
55**99
^5577*
555041
536J04
557567
55*627
555899
555167
55645*
557695
128
117
117
126
558574
5598*9
54«>79
54*5*7
545571
558699
$59954
541*05
54*45*
145696
558825
540079
5415*9
541576
545819
558951
540164
541454
54*701
545944
5448^2
546049
547*8*
54851*
549759
544954
546x7*
547405
548635
549861
545059
546296
547529
548758
549984
54fi85
546419
547652
548881
550106
126
i*i
125
1*5
124
124
1*4
12}
12}
llj
550839
552059
555*76
554489
5556^9
5 56905 I
558108
559508
560564
561698
550962
5511S1
555598
554610
555819
551084I
552}03
5555x'9
5 547^5 »
555940
551*06
55*4*5
555640
5.5485*
556061
5515*8
55*547
555762
554975
556181
122
121;
III
121
557026
558218
55^4*8
560614
561^1
557146
558349
559548
560743
561936
557*67
558469
559667
560863
562055
5575871
558589
519787
560981
561174
1(0
110
120
119
119
561887I
15640741
565157
566457
567614'
563006
564191
565376
563125
564511
565494
563244I563562I
566555 566673
56775*1567849
5644*9
565611
566791
f 67 967
564548
5657*9
566909
568084
1x9
list
1x8
1x8
118
^ J
JlheTahU ofLogarHhmu
N|| -o I r I a*»| 314
^70
57^
171
J74
5^8202!
^70Hl
571709
57**^7^
568 5 i>
56949
570659
.571815
1571988
56^4561568554
5697*5
570893
571058
569608
570776
571^94^
575104
56M7I
56984X
571009
- 57*174
57?U9 575^36
J75||57403i]574H7\574i^?|
J76I 575i88J5755o^l575'4i9
3771 f7^J4M57^457p7^57i
3781:^749^
J79II578639
577^071577711
578754^78868
5743791
575534
57<^<587l
5778361
578983
'574494
57 5649
57^^02
57795*
579097
J 86
381
384
579784
580915
582063
583199
1^84331
57989815800x1
5810J9 581153
581177
583-3**
584444
582191
583416
584587
580126
581267
582404
583559
584670
580141
581381
582518
583652
584783
J85
f86
387
^88
?9o
391
3^2
393
394
585461
58-6587
fa77ii
588852
58 f 574
586699
587823
588944
589949I590061
585799
586925
588047
589167
590284
591665
59^*77
593286
594393
595496
591176
592288
593397
594505
595606
585686
586812
587935
589056
590173
591287
594399
593508
594614
595717I595817
5968x7159^927
5979*41598024
599009
600101
601 191
59X 399159* 509I
591509 591621
593618 593719
5^94714 594834
595937
597037
598134
5991191599118
6002x0 600319
60119^1601408
■»»■■<
>^^r
— *a
•5 1^ 1 -7 ;1 ^8 I 9 II D
56^8905
$70076
$747x6
575»«o
577052
5781*1
5707^51
5.7 1^5 9!'
575^84
574^4^;
575^
577147
I7<f3'09
57 147^
in7S9
5%%^7
570^:^1
58.1495 5.81608 ^^tflr%
5-8'2<6ji
585765
.11" - — ■'^■— — —
ffi|6oi4
5^71^9
589^^91
518-2,745 582.^58
535oo9f5^rJii
5*o^t^8o«i^ii
f8-i'97z 5.8'5t:*^5
f 84105 584iii^^
586157
587261
588384
.^., l?^9foJ
550f07|5^d6lp
59J'7JJ.
59J950
5950551
596157
f8^24^ff8l36^
f8849f'f 88608
59«7?tl5^««4stf
f8«4fi?il^
5887191
589858}
59e^^5
5^t»4J
59*954;
59406 J'
^9"5'i*i5
»9t^55
59je64
5H^7J'
^95*7^
596^j59^37r
5^id6il
594i^J'^
59^80*
597 M^(59n5^|59-7J^^]!? 9747^'
'598i4?l598?55 598462' 59^57*
5995?7 599446 599556 599^6:5
60042816005 57l6oo64,6|6oo755
^?.^±^j7l6o jj^>5 »6o'^7l4t ^oi^Al
!597td^^xto
^9868iiiio
5997741 ibp
16od8^!4J 109
i
The Table df Lo$tmthms.
Nil
i « 1 , 2
I 9 I 4
.HidB
■•^
60a,o59|^oti69
6o5i44Uoj*53
^041161604^34
^053051605415
60638 11606489
6oir77|6ox386|
603 36 1 (60 3 46 91
6044411604550
6o55ii|6o56i8
606596I606704
60x494
605577
604658
6057 j6
606811
[60745516075611607669
|6o8 $i6|6o863 3|6o87 39
1609 5 94I60970 11609808
I6vo6'6o{6i0767l6io873
161x71316118191611936
607777
608847
609914
610979
6 X 1041
607884
608954
6iopzx
611086
61x148
6.IA784
613841
^14897
■615956
6 118-8916 11 996
613947J614053
61500^615x08
6^6o55|6i6i6o
f6i70ob|6i7io5|6i7iio
613101
614159
615113
616165
615x07
614x64
615319
616370
ix73i5|6i74i9
4»5
4»8
^^$)Ah
6i8o48|6i8i53|6 18157
^19093 6x919816x9301
610&36
6x.ii7^
V114
61Q146U10344
611180I611384
6ii3iS|6x»4ii
618361
619406
610448
6x1448
6x1515
618466
6195x1
6x0551
6x1591
6xx6i8
4io«
4*M
411
4*3
4»4l
6131491613353
614181
^15311
616340
1 617 366
614385
fi54J5
616443
613456
6x4488
615518
1616546
613559
61459^
6i5$ix
616648
6i7468}6i757i
■*«i
4»5
41^
4J'7
418
U^9\
618389
619409
630418
631444
631457
618491
619511
6305.19
13*559
618593
619613
630631
631647
618695
619715
^J07»
63^748
jieTable ofLogarithMs,
5 1^1 7 1 8 1-9 II D
60260^16011x7
6oj6i86;6o»j754
6oj^y66
60*5844 605951
606919
607991
609061
610128
611x91
604874
607016
601819
60^901
604981
606059
601918
!So4oo9
605089
606x66
607 14X
60^0^6
6041x8
605x97
606174
607^8
1 08
X08
108
X08
107
608098
609167
6xbi34
6x1198
6x115416x1559
608105
609174
6X0341
6XX4O5
611466
6083X116084X9
6093811609488
6XO447I6XO554
6xx5xil6xt'6^7
6x15711611678
107
107
107
106
106
6x33x3
614369
615414
6i54»9
^14475
^15519
6x6476 6x658
6x3525
6X458X
r6i6686
617525 16x76191617734
6x3630
6x4686
6x5739
6x6790
6x7839
613736
6x4791
6x5845
6x68^5
6x7943
106
X06
X05
105
105
6xJ57s|6i8676 618780
6196x5 6197x9 619814
610656 610760 610864
61x695 61x799161x902
611711I611835I611939
6x8884
619918
610968
611007
6x8989
6100^2
611071
611II0
,6130411613146
105
XO4
XO4
104
104
614798
615827
626855
627878
«awi
625869
6249OX
625929
626956
617979
^iJ973
615004
616031
61705^
618081
614076
615x07
616135
61716^
618x85
614x79
615109
616137
617263
618187
103
103
103
103
loil
619001
I63001X
63x038
651052
629104I619106
618899
629919
1650956
P»95i. , ^- ,.,.-,,. . .^
\6n96n65^o64|65.u65l655i66l65iignioi
650115
63XX59
630224
631241
^3*153 652255
621^508
650526
65x3
651
lyr
101
101
ipi
XOI
^3
f
u^
Ml
Tkc Tabic of LpgarHhmf*
N|i o I rl 2.. I ^ I 4
I—
^^4477
934S78
($36588
4^3^^437589
^33^70^33771
634679
63^^8.5
636688
6^7689
;^JBw|Bi^Uj8589l6386»9
|SJ^6
|6.4P4S:X
'64.^475
6395i^6
6405^1
64x5^.3
630686
64a68o
541671
P4266z
^34779
635785
636789
637789
658789
639785
640779
1^41771
64x761
<53387i
634880
635886
636^^9'
637889
638888
639885
64087
^41*71
641860
HP.
44^
443,
44
4^1
P444-J 9
<^43if.i
H4537
6455x1
643650I64J749
^46404 646501 -,,^
.^+7-^23 1^47431]% 179
64^6 I 9
646599
44 5|
#4^
447
44»;
f.49^'
f5a
4SI
4H
;,
6^83^0
^4?ii5
^So3<)8
653x13
^54177
65,5138
656098
6-57056
648458
64943 X
650405
651375
^51345
^53309
^142-73
<^5fx35
656x^4
M555
6495x9
65050X
^5M7J^
6J2.439
^44734
^457" 7
6496x7
650599
651569
65x536
643847
544833
645815
-H777
^774
750
653405
654369
9Jf3JJ
656x89
65350s
654465
655417
657*47l<^5734J
648
649724
650696
6^1666
65x^33
653 59«
654561
9555x5
656481
657438
+ ^1
k56
4S8
6580? J
6s8$^5
65>-9/^
658i.o7jf58xox
659069
66004 1
6^0960
659x55
6 60 J 06
i66;o55
56l9cy7rl66xOOl
658x98
659x50
660x01
661 149
661096
960x96
«f*4J
6^191
irrimri r r -■ i.
The TMc of Logarithms.
S I 6 \ 7 I 8 I 9 li
^;8988
,40978
654075
6j5o8i
656087
657089
658089
^^07 51^34^7^
655181 655185
656187 656188
6571891657189
658i89|5;3$i89
^5437^
635383
6^6388
657589
658589
loo
100
100
100
9P
mm
659088
640084
64IO77
64X069
643.058'
659188
640183
641 177
64x168
645156
659187
640185
641176
641167
643*55
659587
640581
641575
641566
^431
66
54I
99
99
99
99
9^
'4^94^
H495 ^
>45913
.46894
644044l644i'43
645019
64601 I
646.991
^478711647 969
645117
646169
644141
645116
646108'
647089I647187
6480671648 16 5
■»-»i
^48848
)498ii
»5o795
'51761
551719
> 5 3^95
^54658
6489451649045
649919
650890
M1859
651816
650016
650987
651956
651913
649140
650115
651084
651053
653^^9
653791655888
654754^548 5p
^5 5619)65 5715 655810
^56577 656675 656769
>57534,657^»9 ^57715
,58488
$59441
>6o59i
S6 15.59^
^611
658584l658'679
95.9556 659630
660486
661434
660581
661519
661475
653984
654946
655906
656864
657820
658774
659716
660676
661613
6^1569
I 4
644540
^453^4
64© 5 06
647185
648161I
649137
650110
651181
65i«49
655116
654080
655oifi
656001
6 5 6960
6579x6
9«1
98'
98
98
•95
'97
97
97
97
91
7^
96
96
96
96
658869
6598£i
660771
661718
661661
9?
95
95
95
95
s
N II o I I I 2 I 3 ) 4
• »
The Table of Logarithms. ;
■^' ■ « '
4^0
461
4^.2
45 J
465
466
467
4^8
469
666518
i^6i8$2
6647^6
666611
662947
663889
^^57^9
666705
663041
66^985
664924
66^S6z
6667^^1
665155
66^078
66501S
^^74 S 5
66838^
66^317
670146
671173
667546
669409
^7PJJ9
671265
668571
6,69505
670431
671358
^^7733
66S665
670524
671451
»..«.
470
47 »
471
47?
474
671098
673021
673942
674^61
47^
476
477
478
479
480
■48.
482
483
676694
677607
678518
679428
680336
672190
6t3ii3
674034
^7495?
675869
676785
677698
67&60.9
679519
68b426
672283
673205
674126
675045
675962
676876
677789
678700
679609
680517
^73'J7^
^73297
674218
676053
676968
6,77881
678791
679700
68060^
667S16
66875J
6706 17
^7I54J
671467
675589
674509
67^228
67(^14^
^77059
677^71
678882
67^7^1
6806^8
6i!Ei24i
632145
683047
683947
684845
681332
682235
683137
684037
684935
681422
631316
683227
684127
685025
681515
682416
685317
684217
685114
68x603
682J06
68.5407
684507
685204
^85l
486
I487
488
li2
6«5742
686636
687529
68,8419
68930J9
^85?3i'
686326
687618
^8509
685921
6868 1-5
687707
688598
689486
686010 686099
'686904
687796
68S687
^89575
^8^94
687^85
688776
6891664
The Table of Logarithms.
9T
• T"^
5 I ^ I 7 • 8 I 9 II D
664171
666049
6665^86
6655x4
664166
665106
666145'
667079
665418
664559
665199
666157
667173
665511
664454
665J^^
666551
667166
665607
664548
665487
666414
667 5 59
66^919
668851
669781
670709
^71656
"^■'^■^'■*"* ■
67^559
675481
674401
67fgi:9
676156
677151
678065
678975
679881
680789
668015
66894s
670802
671718
671651
^75*574
674494
67631 8
677141
678154
679064
679971
680879
6681061
669058
669875 669967
670895
671811
66^199
669151
670060
670988
671915
668195
669114
670153
671080
671005
i^7i744
675666
674586
,^75^05
676419
671856
673758
674677
^75595
^76511
671919'
675849
674769
675687
676601
^7733?
678145
679155
680063
680969
6774141677516
678535 678417
679146
680154
681060
679537
680245
681151
681695
^81596
685497
6843^6
685194
681784
63 168 6
685587
684486
685383
681874I681964 ,,
681777 681867 681957
"* ' 685767 685857
684666 684756
681777
685677
684576
^85473
681189
687083
687975
688865
68975?
686179
687171
688064
688955
68984
*'*5^7J -'"^^05 u«)%/)i|
r ' ' ■ I I M^ ■ ' - ■ I '■ ' " '
$863681686458 686547
687161 687351 687459
688153 ^88141 688331
688i5j
68904
689930
689042 689151 689110
A^^^^^ 690019 690107
94
94
94
94
94
93
93
93
93
93
v
91
9*
9*
9>
91
9»
91
,91
9*
9»
9*
90
90
90.
?f
89
89
89
8,
I
The Tabic of Logarithms.
• mm
Nil o 1 1 1 3 j' 3 I 4
4j^o
491
4941
690196
69108 1
691965
69x847
6^5727,
690x85
69.1 169
69x055
6929^5
6938x5
6903:7^69046
691x^8
69x142
69gox;
693903
691347
691x29
693111
6939^1
^9i4?f
59Z318
65^4078
491
496
497
498
499I
1694605
695^482
697X2$)
6^8101
694695
695569
696444
6973J7
698188
Mi''<Wl «
500
502
503
104
698970
699838
700704
7OI568
702430
699057
699924
700790
701654
70x5«i7
694781
695657
696531
697404
698275
699144
70601 I
700877
7 1741
702605
fa«IMMHi
fo5
506
507I
508
J09
705x91
704151
705008
705863
706718
704236
705094
705949
706805
7054^3
704522
705179
706055
70688B
69486I
<^95744
696618
697491
698362
699281
700098
700965
701827
702689
705549
704408
705265
7o#ixo
706974
69583X
^97S7^
69844P
^■^.^^ if
699J17
700184
70104^
701913
702775
5«o
511
5I2
51I
5^4
n5
516
517
518
707570
708421
709269
7x0117
710963
707^55;
708506
7^9J55
710202^
7 II 048
711807
71x649
715491
714519
7^5167
711892
712754
7i?575
714414
7^5x51.
707740
7085^1
709459
710287
ZII1J2
7II976
712818
715^59
7 1 4497
•<w >1 I.' I- ■ I'M
707826
708676
709524
7IO57I
711X17
71X060
712902
715742
7I458I
7!.54i8
705635
704494
705550
706206
707059
707911
708761
709609
710456
7 1 1501
71x144
712986
715826
7 1466 5
715501
The'tahk of Logarithmf.
5-15 I 7 I 8 I 9, II D
690659
691514
691406
69x611
69*494
694154
690816
691700
692583
695463
69434a
690905
691789
692671
694429
690993
691877
692759
693639
^94517
89
88
88
88
88
695044
695919
698535
695131
696007
696880
697752
698622
695219
696094
697839
699404
700271
70H36
701999
702861
^9949 I
700358
701222
702086
70*947
699528
700444
701309
702172
695307
696181
697555
697926
698706
700531
701395
7.02258
^95594
697 I 42
698014
698885I
703033I703119
699751
700617
701482
702J44
703205
^8
.87
87
87
^7
87
87
86
86
86
703721
704579
70.5436
706191
707 144
703807
704665
705S21
706376
707219
703893
704751
705607
706462
707515
703979
704837
70561^3
706547
707399
704065
704922
70^778
70663a
707485
707996
708S46
709694
710540
711385
70^081
708931
7097791
710625
711469
708166 708251
709015
70986.3
710769
711554
709100
709948
710794
I711639
708336
709185
710033
716879
7U713
712229
713070
J715910
714749
1715586
712313 7123971712481
713154 713^58 7Mii5
713994714078 714162
7148331714916714999
715^69171575 3 1715836
■ I ■ » I ■ ■■! I *^ I I M M!
712566
713407
714246
715084
715919
86
86
86
85
■
8J
8<
8J
84
84
84
84
84
^^
I
_ 1 I M
TheTable of Logarithms,
N II o, I I I a I 3, I 4
%Z0
514
5*5
5*9
5J0
551
5ji
555
534
535
536
537
538
539
540
541
542
54?
544
71600J
7168J8
717^71
718501
719331
716087
716911
717754
718585
719414
716170
717004
^17837
718668
719497
71^154
717088
717910
718751
719579
716JJ7
7i7i7lj
718003
718^54
7 19^^31
710159
710986
711811
7116^4
7*3*456
714176
715095
7*591*
716717
7*7541
710141
7110^8
71189?
711716
7*353^
7*4358
715176
7*5993
716809
7*76*3
7*03*5
711151
7*1975
711798
713619
7*04P7
7*J^*33
711058
711881
7*3701
7f049<
7^1316
7XZI40
7x19^3
7i37«4
7*4439
7*5*58
716075
716890
717704
7*45*i
7*5539
716156
716972.
717785
7Z4604
7»T42'*
726138
7*7053
717866
7*8354
719165
7*9974
730781
73^89
73^394
733197
733999
734799
73559$^
718435
719146
730055
730863
731669
718516
7*9?*7
73oi3v6
730944
731749
728597
719408
730*17
73I024
731830
718678
7*94891
730198
73H05
731911
731474
733*73
734079
734879
73x5679
^545
546
;547
548
[549
736397
73719*
737987
738781
71957*
736476
737*7*
738067
738859
739^51
73*555
733358
734159
734959
735759
736556
73735*
738146
738939
739731
733518
734319
735119
735918
73i^635|73*7M
733438
734*39
735059
735838
736635
737451
7381*5
7J9018
739809
736715
7375xi|
738305
739097
739889;
The Table of Logarithms.
5 ~7*7^ s"
I642X
172,54
1S086
'18917
7x6504
717358
718169
718999
197451719818
716588
717421
718155
7I908J
719911
716671
717509
718336
719165
719994
no 5 73
72I398
72x221
723045
723866
720655
721481
722305
7231Z7
723948
710738
72x563
7-22387
723209
724029
7208211720903
724685
7*5503
726319
7*7134
7*47^7
7*5585
7 26 40 I
727216
727948 [728029
724849
725667
726483 726564
7*7*97
728110
721646
722469
723*91
724112
■^--- .'
7**49ii
7*5748
7*7379
728191
72I728
7*?^55*
7*3374
7*4194
7*5013
7*5829
726646
7*7459
7*8*7i
83
82
82
82
82
82
82
82
81
81
728759
729569
730378
728841
729651
730459
728922
7*973*
730540
719003
7*9813
730621
751186 731*66 731347 7J>4*?
73x9911732672173215*573**33
72908411 81
7*9893 8ij
750701 8x
731508 81
732315 81
■■MM W*
75i79'6
1733598
I7S43 99
735199
735998
73^795
737590
738584
739^77
751876
755^7^
734479
735*79
732956
733759
734559
735359
736078I756157
733037I733117I
73583917339*9
734659
755459
736*37
734719
755519
756517 I 80
80
80
80
80
7368741736954
737669 757749
758465 73854^3
75705417571x5
757819I757908
758612I758701
/:»7-//i739*56 739535 759414 739493
7 59968 17400471740116174010$ I740184I
i
. -^ ..-.r - ' — •
The TdbUof Logarithms.
■ T '
Nil
I I I si )' I 4
5f4
741152
741939
74J5 S^
74044*
74^*3^
742018
741802
74J588
740521
74.1509
742096
742881
743^67
740599
7413881
742175
742961
74574V
74«>^7«
74" 54
74J039
743S23
555.
55^
<S7
55»
559
744193
745075
745855
746634
747411
744371
745r53
745933
746712
747489
744449
7452J1
746011
7467^9
7475^7
7445x8
745309
746089
746868
747^45
f6o
5^1
562
5^3
5J64
74818817,48 i66
748963
74973^
750508
175x279
749040
749814
75o5»6
7513^^
748343
749I 1 8
749891
7 50663
7ti433
748421
749195
749968
750739
751510
744606
7453^7
746167
746^5
7477*«
741498
749*72
750045
75;?«r7
751^87
.5^5
566
567
568
569
752048
752816
755583
754543
75JII2
7^*»i5
75^89^3
753^59
7554*5
755^89
751202
75296]^
75373^
754501
755265
75**:^9
753047
753813
754578
755341
75*3^
7531231
755«89
754^54
755417
570
57J
574
UF55875
756656
175759^
758155
758911
755-9^M
756712
757471
7582^0
756027
756788
7575-^8
758306
758938I759063
756103
756864
757627
758382
759^59
75^179
756940
757699
758458
75:93^M
575
57^
577
578
579
7596681759743
760422
761176
761918
762679
760498
761151
761003
7^*754
760575
761316
761678
761819
7*9894
760649
761402
762153
7629)^4'
7599^5
76071 J
7614771
76iiiF|
76297tr
Tke^aMe of iogaritbms^
■ ■ I 'Ml
f 1:^ I 7 L 8 I 9 IID
1740757
41546
174^53*
l74?ii8
|7459o»
740856
741624
74241 1
745196
)743979
744684
7454^5
74^145
747023
[747800
748^76
-7495491
750123
750894
75166^
752433
753199
J755966
754730
755494
744761
745543
746313
747 lOl
747878
y409t5
741703
742489
743275
744058
744840
745^21
74640 )
747179
747955
740994
741782
741568
743353
744136
741073
741860
74*647
74343 »
7442^15
79
79
79
78
78
7449*9
745699
746479
747256
748033
744997
745777
74^556
7473H
748110
78
7«
>8
78
78
748653
749427
750199
750971
751741
7487?!
749504
750277
751048
751818
748808
749582
750354
748885
749659
750431
75^125 751202
7518^51751972
\
77
77
77
77
77
752509752586
7532-77
754042
754807
755569
75335-3
7541191
754883
75 5 ^4^^
752663
753429
754195
754959
755722
752739
753506
75427.2
755036
755799
77
77
77
76
7^
756156
757016
57775
58533
5929a
756332
757092
757851
758*609
7561^08
757168
757927
758685
759366.759441
756484
757244
758003
758761
759517
756560
757320
758079
758836
759592'
76
76
7^
7«
[760045
60799
761552
762303
760121
760875
761627
762378
763128
760949
761702
762453
7.^3203
760272
761025
761778
762529
763279
760347
761101
761853
75
75
7J
7«
u
Tbe Table qf Logarithms.
N||o|iia''3«4
53o
581
584
7^54»8
76417^
76491^
7656^9
766413
76.41$ I
764998
7^5743
766487
7^JJ78
764316
765071
765818
766561
7^3^53
764400
7^U47
76$89i
585
586
U87
588
767156
767898
768638
769377
770115
7672,30
7^7^71
768711
769451
7701*89
767JO4
768046
768786
769525
770163
767379
768119
768860
769599
77033^
765727
764475
7652x1
765966
766710
767453
768194
768934
769673
770410
'590
591
593
^4>4
770851
771587
77^321
773055
773786
770916
771661
77139^
773118
7^5859
770999
7717,34
771468
77310J
773933
771073
771808
771541
773»74
774006
771146
77i««i
7/x6i5
773348
IF4079
^9S
59^
598
^99
774517
775146
775974
776701
777417
7745^9
7753»9
776047
77^774
777499
774^^3
775391
776119
776846
/77571
77473^
775465
776193
776919
777644
774809
775538
776165
77 ^99i
777717
5oo
Soi
60 a
5o3
5o4
778151
778874
779596
780317
78x037
77812417781961
778947 779019
779669
78/0389
78 1 109
779741
780461
781181
778368
779091
779813
780533
781253
778441
77916J
779884
780605
7813*4
5o5
^07
5o8
781755
782473
783189
783904
784617
78.1827
781544
783260,
783975
784689
781899
.782616
783331
784046
78475^^
;^8i97i
782688
7^3403
7841x8
784831
78za42
782759
783475
784189
784902
Ti)e Table ef Logarithm.
1
■<— «
5 \ 6 \ 7 i 8 1 9 II 2>
764^49
7(56041
766785
768268
7690^8
769746
770484
77^119
77195^
772688
77 54tx
774152.
774881
75^5610
77^3?8
^77064
777789
763877(765952
764624
76557P
766115
766859
767601
7^8541
769082
769820
7705^7
764699
765445
766189
76693 3 1
767675
768416
769156
769894
770651
764027
764774
7^5519
766264
767007
764101
764848
7^559.4
7663^8
767082
767749
768490
769229
769968
770705
767823
768564
769^^3
770042.
770778
7712-93
772pa8
1^7a76i
77U94
7742'i5
771367
772102
7735^7
774298
77^440
771*75
772908
773640
7745'7»
7715H
77.>i4«
77^9?^
7737«!
774444
774955
775683
776411
777 1 ^-7
777862
778513
779236
7799^^
780677
781396
778585
779308
780029
780749
781468
781114
|78'283i
783546
784^^1
1 784974
782186]
78x901
783618
7843^32!
1785045
775028
775756
77^483
777209
777934
778658'
779380
780101
780821
781535^
■ » —
782258
782974
78.3^689
784403
85116
77510b
775829
776556
777282
778006
775173
77 59P*
776629;
777354
778079
778719
77945*
780173
780893
781612
778802
779524
780245*.
780965'
781684
75
75
'75
74
74
74
74
74
74
r4
74
73
-73
•73
: 79
73
73
.73
7-3
71
72
71
<7»
7^
7^
7813291782401
783046I7831J7
78376^17838^2
7844751784^4^
785187 785159
P
2
71
71
71
K
N II © L I I 3 I 3 I 4
Jte Tabk rf L^arhbms.
^19
6x1
6,}
^X4
7S6041
786751
787160
7S8164
785401
786111
7868x1
7«547i
78618^
786'S9j
787^11787^01
7»5543
786154
786964
787^73
7881^91788 J09l788}8 1
i
^15
616]
617
j6;8
619
788875
789581
790*85
790988
79:1691
788946
789651
790^^
791059
791761
789016
789711
790416
7911*9
7918JI
789087
789791
79049^
791199
791901
785^15
7863x5
787035
787744
788451
789157
789863
790567
791^^9
I79*f7l
6x0
!6n1
|6xi
6x4
79*59*
795091
79J791I
794488
795185
79*4^»
793161
793860
794558
79*53*
79J*Ji
7959^0
794^*7
791601
7955^1
793999
1794^97
79*^7*
791371
794069
7947^7
795*54l7953*4179539M795463
615
?6x8j
\^9\
795880
79^574
797168
797959
79865 X
795949
796644
7^7??7
798019
798719
796019
79^713
797406
798098
798789
796088
796781
797475
798167
798858
79^158
79^851
797545
798236
7989*7
fS9
799MI
800019
^00717
801404
801089
799409
800098
800786
801471
801158
799478
800167
800854
801541
80^116
799547
8001^36
8 0091 J
So 1609
801195
799616
800505
800991
80x678
80x363
801774
803457
804139
804811
805501
801841
803515
804108
804889
805569
801910
803594
864176
80^95^
805637
801979
803661
804344
805015
805705
803047
803730
804411
805093
80 577 J
The Tahk »f Lo^aiithmt.
l'm»m0amim
5 I 6^ I 7 I 8 l.:9 iInO
785686
7JB6596
787106
787815
7«85i;l
789x18
7^9911
7906J7
791319
79104.1
785757
7J6467
787177
787885
788593
7858x8
786538
787148
787956
78866^
785899
786609
787J19
788017:
7!^«734
7?5970
78668b
787189
78809P
788S04!
71
71
71
71
7891.99
7900Q4
790707
79M<»91
791111
7895^9
79P074
790778
791480
79>^8l
789459
790144
790848
791550
79>*5i
7?95«0'
7901-15
7909>8
79»^*o
79*3*>
471
70
.76
7^0
79*74«^
79H4J
794M9
7948 J 6
7955J1
" ■ '
79^2^17
796911
797^14
795305
798996
791811
79J511
794169
794906
795601
791881
793581
794^79
794976
795^7*
7919U
793^51
794349
795045
795741
79^0^^
I7937M
7944*8
79fMf
7958l<t>
796197
79^990
7 9768 J
798374
79906$
79^366
797P69
7 977 5 i
798443
799134
796456
797811
79851*3
796(P5
797119797198
797890
798531
1799105179917^
"^^■•'
-•^
799685
I$ooj73
80I061
801747
.80145 1|
' L 'III II ■
805 I 16
803798
1 04480
lo5l6i
io584i
799754
800441
80x1^9^
18018^5
[80^500
805x84
805867
804548
805229
8o5j^8
7998*3
8005x1
801198
801884
80M68
799892
800579
801166
80195*
801657
799961
800648
80 I 5 55
80101 I
801705
805251I865511
805935
804616
805197
805976
805389
8o4ao5l8o407i
8047 5 5
805433
806111
804685
8055^5
S 06044
M
fa
70
69
69
69
69
69
69
69
6%
68
68
68
68
68
TU Tabie of Logarithms.
N II o 1 I I 2 I 3 I 4
64b
641
641
64J
644
^'
^4^
647
<54?
^4P
806x79
866858
807135
8082II
|8o8886
806148
806^16
80760J
808179
808953
8063
806994
807670
161^06384
809011
S07061
807738
808346^808414
809088
806451
807 1x9
807806
'808481
809x56
'■o^
869559
810133
810904
8M575
809617
810199
8 1097 1
1811641
809694
810367
8x1039
811709
Siii45|8iiji^8ii579
809761
810434
8x1x06
8 X 1776
81x445
^50
65J
*5*
«53
6C54
8119^3
8x35«i
814148
8149M
81^578
8x198 <)
813648
8143x4
814979
815644
*^55
656
^57
1658
^59
660I
661
661
663
664
8x6141
8x6904
8x7565
818116
8i^a85
8x9543
8ibiot
810858
811514
811468
816308
8169x0
8i763i
818191
818951
819609
810167
810914
811509
811133
813047
813714
814381
815046
8157XX
81637^
8x70.36
817698
81835S
|3 19017
8x3x14
813781
814447
815113
815777
8x6440
817101
8x7764
8x8414
8x90^3
809829
81050I
8 X X X7 3
81x843
8x1511
8x3x81
813848
8x4514
815119
8x5843
8x6506
8171^9
8x78id
8x8489
8x9149
819676
810335
810989
811^45
811199
819741
810599
8iio55
81x709
811364
8 19807
8 10464
811110
81x775
811419
665
666
667
66%
8ii«ii
813474
814116
814776
815416
1811 87
8i3539
814191
814841
8z549t
811951
813605
814156
8 14906
813018
813669
814311
8 1497 X
8i5oixr
813085
8^3735
814386
8i5Qj6
815686
r
TheTahle ofLegtrtthm, \
5 1 ^1 7
S07197
^07873
806587
807264
007573 807941
808549J808616
8092231809290
8098961809964
810569 810636
806655
897^1
868008
808684
8093581809425
8067231806790
807399807467
8o8ofT<$ 808143
8o$8|8
80949
808076
8087 1
^7
I ^7
811x39
811909
811307
8 1 1977
812646
8I0098I&IOI65
813247
8I59I4
H58I
15^46
15909
810031 810098
8 1 0703 810770
8 II 374 811441
812044 812H1 9x^178
8x27131812779181^847
8x0837
8xiyo8
8x^178
^1
67
67
6j
Zi
S
8
813314
81398 1
814647
8153x2
8x5976
8i338x
8x4048
8147x4
815378
816042
813448
8141x4
814780
815445
8x6109
81351411
8x4i8x|
814847
8155H
8x6175
67
67
66
66\
816573
817x35
817896
818556
819215
819873
820529
821X86
82X841
822495
816639
8X7301
8i796i
818622
81928 1
8x6705
817367
8x8028
8t8688
8x9346
816771
8174J3
818094
818754
8x94x2
8 199^9
820595,
821251
821906
822560
8x683
8 17499
818159
818819
819478
66
66
66
66
66
823x48
823800
824451
825x01
8232x3
823865
8245x6
825166
8258x5
823279 823344
823930823996
824581 824646
825x31 825x96
82$88of825 945
823409
824061
82471;!
8x53^1
826009
6i
■taak^AOMfc
■MM
m^mmtm
TkeXi^k ^ tUfgrnnthmi.
N II oil
I
I
-t
a I 4
•Mite *■
^261^9
--^v , «*/-r>T --7499 ^^-TS^J «»*70i»
8ttoft5 ti%6*f^ ti8i44 828269 ^1817^
- -' * • - Jli87«9|8x885^8t89i8
8t<j54
Si^d75|8i^i39|8k6204 ^ ^^^
82671^1816787 826852 826917 8269S1
8275^9 8274^4 827499 827563 82762!
8280159280798281^^828200'" "
828659 $28714
• »'^>y oie7*)f •i»7»y]02o«^5-j
829^^1829368 829432 829497
82^947 830011 830075 830159
83058^ 8306IJ S?07I7 830781
^--o-- '*'-J58$^l4tr
998 $i*o6i
- - "
029504
82^947 S3ooif|230o
830589 83061^ S307
1831249831294 8313
5318^98319348319
II2956
83020^
830845
831486
8321x6
, \%%w
85250^ 832573|;8t>^5^j83i70o
833147 833211 83^275 833558
833784 835^48 855s^i2 835975
^8Hl$i3442r 834464183454^ 8346ir
^84ll885o56|&35ii^a^^i«5 835247
■» J M l M
8'356$t
a**'
832764
833401
8J4O39
854675
83^5110
836324836387
85<^j9^7|8j70i9
8375*8
831817
8j64n
837083
i^375«o $37^51857715
8 3821^18 3ei82{85&345
835881
8J6514
837146
8 57777
8 38408
^55944
856577
837209
85784^
83847,1
8f9^9
839478
840106
^407 3 3
838912
^39541
840169
840796
I841J59 8414*5
838975
,839604
840252
840859
1^41485
839033
839^67
840394
840921
841547
839101
839729
840357
8409&4
841609
841985
842609
845155.
845855
S44477
842047
842672
*45»95
8^3918
M559
842109
M754
843557
843979
-18 446^1
842172
842796
845419
844041
I44664
The Table of lagarithoUi
S .1. 6 I, 7.1 8 1 9 Jl,p
8L7046
9x76^1
8»898a
816464
817111
827757
8x8401
829046
826528
827175
8^27822
828467-
8 291 I I
826595
827886
8285^1
829175
826658
827305
82795^
828595
8^9239
829615
8J0268
^30909
831549
823189
829689
830332
830973
831614
832253
»»9754
850396
•31037
831678
832317
829818
8304^0
83 1 102
831742
83.138-
829862
830515
831166
83r8o6
83*445
8.32828
8^34616
834103
834739
835?73
831892I831956
833529 %ZZK<iZ
814166
834802
18 35437
8^3593
834229
834866
835500
833019
833^57
834194
834929
835564
833083
833721
834357
834993
835^17
836007
836641
837173
837904
838534
836071
836704
837339
? 379^7
838597
836134
8367^7
837399
838030
838660
839164839127
839792839855
840479 840482
841049 841109
8416721841735
83928
83991
840545
841 172
841797
836197
836830
837462
838093
838723
839351
839981
840608
841234
841859
836261
836894
837515
.838156
838.786
839415
840043
840671
841297
841922
842*97
842921
843544
844166
18^88
841359
842983
843606
844229
844849
842432
84304^
843669
844i9i
844912
841484
843108
843731
844353
844974
841547
843170
843293
844415
845036
61
H
«+
64
64
<5j
6i
6i
-
6i
it
6x
6i
J
TheTabk of Logarithms^ '
Nil; o I I I a 13 ,4
7po
7^)1
7b
704
%
8450^8
84J718
$4^337
846955
«4757S
845160
845779
846599
847017
847654
845111
845841^45904
846461
847079
847696
845184
846515
847141
847758
84^4^^
845666'
8465»f|
847 20 x'
84781^
705
706
707
708
709
846189
848805
849419
850655
8^0646
848151
848866
849481
850095
850707
8485x1
848928
849541
850156
8 50769
.- *i
84845 y
849051^
849^^$
850179
85089X
710
711
711
713
714
7m;
716.
7^7!
7l»l
7»9l
851158
85i86$r
8"5i479
855089
855698
854306
8549x5
355519
8^56114
^56719
851319
85f95»
851541
85315b
853759
851581
851991
851601
853m
853819
851441
851055
81(2665
853*7*
855881
85x50}
85^114
8517*4
853,339:
853941
85436718544*8
854974
855579
856185
856789
855054
855646
856145
856849
854488854549
8550^5 855r5^'
8557^1 855761J
856506856366
85691085697.0
1
720
711
712
713
714
8f733*
857935
858537
8591^38
859739
857393
857995
858597
859198
859799
857453
858056
858657
859158
859859
857513
858116
858718
859318
8^99 1§
817 574'
858176
858778!
8593791
859978
715
716
717
718
719
860338
860037
861534
8611 5 1
861718
860398
860996
861594
861x91
861787
960458
861056
861654
86ii5]r
861847
86o5x8/86»578
86iix6i86ii76
861714
861316
861906
861773
861369
86i966
■ '' II I ■■ ■'■ I I I. ■ ■
Tl&e Tabk of Logarithms.
5 I 6 I 7 I 8 I 9 l)D
45408
4^pxd
^6646
I47164
I47881
845470
846080
8467^8
847^x6
347943
84^552.1
846151
847^88
848004
845594
846213
846832
3 47449
848067
84^656
846275
846894
847511
848U8
^48497
(49111
{49726
^to5J9
J 50952
5515^4
J5SI75
851785
85'3?94
B5400
84855913486^0
849174
849788
850401
8 5 10 14
851625
851*?^
852846
855455
854063
849*55
849849
850462
I851075
2
849297
84^911
8505*4
85113^
848743
849358
849972
8505^5
1851197
851686
852297
852907
85j5i6
854124]
8517471
.851358
852968
853577I
^1854185
851IO9
852419
853029
853637
854245
854609
855216
855821
856427
857031
,857^54
'858236
'858838
1859439
860038
854670
855177
855882
856487
857091
857694
354751
8553J7
855945
856548
857151
857755
854792-
855398
856003
856608
857212
854851
855459
856064
856668
857272
860637
861236
861833
362429
858297 858357
858898 858958
859499859559
8600981860158
857815
858417
859018
859619
860218
85787.5
858477
859078
859679
860278
860697
861295
861893
860757
860355
861952
860817
861415
862612
862489(8 62U9I862608
860877
861475
862072
862668
863.02518630851863144186320418632631
62
62
62
62
62
62
61
61
61
61
61
61
61
61
61
61
61
61
60
60
60
60
60
60
60
60
60
60
I' TheTabk cfLfg/ttitlms.
J
I
^m^mi^
^■mm «4kMHM«M*i^^
?3o'
751
7J3
7341
18^5513
;j5|l86^i87
86,4511
365104
8656^6
863382186344%
863977
864570
865163
865755
864036
864619
865ZIX
863501
864096 864155
864689
86581418^5^74
863561
864748
865181 865341
865933
* I I ■ *■
736
737
7J8
739
866878
867467
868056
868643
866346
866937
867546
868115
868703
866405
867581
868174
868761
866465
867055
867644
868133
966 s ^
867 ii4
867703
8682^1
3683111868879
740
741
741
743
744
86$ki3i|869i9o
869818 869877
G70404
870989
37M73
870464
871047
871631
86934^1
869935
^70511
871106
871685;
86940Q
870579
871164
871748
869466
870053
870638
871113
871806
745
746
747
748
749
750
751
75i
753
754
871156
87*739
8733J''
^73901
871115
871797
87337^
873959
874481I874539
871173
871855
873437
874018
874598
87x33*1
8719x3
873495
87407.6
871389
871971
873553
874134
874656^874714
875061
875639
876218
876795
-877371
875119
875698
87^176
876853
877419
"87fi77
875756
876333
8769I0
87513-5 87519}
875813
876391
876968
877487 877544
875871
876449
877016
877601
755
756
7 57
758
759
<77947l
878511
879096
879669
880141
878004
878579
879153
879726
880199
878061
878637
879111
879784-87984
S 80 3 56
878II9I878I77
878694
8.79168
^880413
878752
879315
8798^8
^80471
lAiW.
rt»iii«i
TbeTdbk of Logarithms.
5 1 ^.. I '7 r 8 I 9 IID
1^642x4
{64808
J6f4oo
865992
864274
864867
865459
866051
7
86^7^9
804335
864926
865519
8661 10
«HMa
"•*»■
8637991863858
864^91 864452
864985
865578
866169
865045
865637
866228
866^58 3
867173
B67762
868350
1^8938
866642
867132
867821
B 68409
^68997
866701
867 191
867879
868468
^690 5 6
866759
867349
86793^
968527
8691 14
866819
867409
867998
86858^6
869173
869515
870UI
870696
371281
871865
869584
870169
870755
871339
871923
869642
870118
870813
871398
^871981
869701
870187
87P871
871456
B71039W72098
8697591
870345
870930
871515
872448
873019
873611
874191
874772
871506
873088
S 73 669
874249
874829
87*564
873 J 46
873717
874308
874888
872611
873204
873785
^74366
874945
871681
873161
873844
874414
875003
87535a
375929
8765P7
'3 7708 3
^7765.9
875409
875987
876564
877141
8777x7
875466
87604
876621
877199
877774
5 876
87551
sot
87667$
877156
^77831
4187
5581
876160
8767 J7
^77314
877889
^1341878191187834918718407
^78808
879381
^79955
^80517
878866.
879459
878914
880013 880070
8,80585 880641
87949r*79555
878981
880127
880699
878464
?7?059
879611
880185
88075*
59
59
59
59
59
^9
19
59
59
59
19
19
59
58
58,
58
58
58
I 58
58
58
58
-58
5a
57
57
57
57
The Tabk of Logarithms,
N\\ o \ I I s 1 3 ' 4
760
761
764
S80814
881^85
881955
881515
88J093
88^871
881441
881011
881581
883050
88091^
881499
881069
881638
883167
880985
881556
3 8 II 16
881695
88J164
881042
881613
88118J
881751
883311
765
766
768
769
883661
884119
884795
835361
885916
8^37iS
884185
884851
8854V8
885983
883775
884341
884909
885474
886039
883831
884399
884965
885531
886096
770
771
77»
773
774
886491
887054
887617
888179
I888741
886547
887 I.I I
8S7674
888136
588797
8^6604
8,87 167
887710
88^191
888853
77i
776
777
778
779
I889301
889861
8904^1
890979
891537
88935?
889918
890477
891035
891593
889414
8899^4
890533
891091
891 649
886659
8^7,i2.3
887786
888348
888909
889469
890019
890589
894147
89I7.05
883888
884455
885011
885587
886151
886716
887275
887841
888404
888965
780
781
781
785
784
891095
89S651
893107
893761
894316
891150
891707
893161
89^817
I89437I
785
786
787
788
I 17 89
894869
895423
895975
896516
897077
8949*5
895478
8960,19
^96581
897x31
891106
891762
893318
893873
894417I
894980
895533
896085
896636
897187
891161
891818
893373
893918
894481
895036
895588
896140
896691
897141
889513
890086
890645
89X103
891760
89I3I7
891873
893419
393984
894538
895091
895644
896195
896747
897I97I
Mb^pdNWU^
TheTabk of Logarithms,
5 I <5 I 7 I B I 9 11 D
(82809
■•V
881156
881717
882x97
882866
88J4J4
88121;
881784
882-354
882923
883491
88x271
S81841
882411
882979
883548J
881^28
88x898
882468
88JOJ7
883605
^83945
I84512
1^5078
I85644
•86205^
884002
884569
885135
885700
886265
884059
884625
885192
8«5757
886321
884115
884682
885248
885813
886378
884172
884739
885305
885869
886434
186773
187336
87898
I88460
189021
r >**«■■
89582
9014 I
90706
91159
91816
'91373
92929
93484
94039'
94f9J
.9514^
[95699
{96251
(96802
^9735*
886829
88739*
887955
888516
889077
889638
^poJ97
890756
89JJI4
891872
1.886885
887449
888011
8885^3
889134
886941
887505
888067
88S629
889189
886998
887561
888123
888685
889246
889694
890253
890812
891370
891928
889749
890309
890868
89I426
889806
890365
890924
89 I 48 2 I
891983 89^039]
892429
892985
894094
894648
895201
«95754
896306
^96857
897407
892484
893040
893595
894149
894704
1895257
895809
896361
896912
897462
8^2539
8930516
893651
894205
894759
89*595
893151
893706
894261
894814
5:
5:
f:
5;
5;
895312
895864
896416
896967
897517
51
5
5:
5:
56
56
56
56
5^
5^
56
5<5
S6
895367
895-919
896471
897022
56
56
56
55
55
55
55
55
51
I
Tbt Tablt ofLegariihmi.
790
79»
in
794
Nil o I 1 I 2^ I 514
897^17
89817^
898715
899175
8998 z I
897^8);
8981^
898780
899^^
899875
«9>79*
898541
89888^
^994'p\^99^9
899985
«97«47
^9^19
«^94
9000^9
'J
795
79^
797
79>
799
800
to I
«o3
804
900367
900915
9J1458
90x063
9<>»547
903089
901^11
904174
90 47 1 6
905156
j|004it|
93096$
901 5J J
90*057
906476 900531
901021 901077
901567
901111
901611
901166
90166119016551902709
903144
905^87
904119
9047^9
90551'v
903199
903741
904183
904814
905364
903253
905795
904337
904^78
90541*
900586
90113 X
901^76
90x22 »
902764
903307
9035491
90439*
90493*
90547*
^*—*'
805
806
807
808
809
9io
811
811
814
815
816
««7
818
ti9
905796
906335
906874
9074^1
907949
905849
906589
906^917
907465
908001
905904
906443
907981
907519
908056
905958
906497
907055
907573
908109
90^11
9«>655i
5^07085
907616
908165
90848 5
909021
909556
91009^.
910614
$0^539190*59*'
909074
909609
910144
910678
909118
90966 5
910197
910731
908646
909181
909716
910251
910784
908699
909>35
90^769
910304
910858
...i-
9txx58
9x1690
911211
91*753
913284
9x1111
9"743
911175
91180.6
913337
91x263.
9x1797
9U323
91**59
9x3389
9x13x7
91x849
^12381
9129x5
9'M43
9x1371
91x905
9»*435
9x1966
mf
The Tabu cf Logarithm. . I
• ••M#»
SI 6 1 7 I 8- 19 11 D
897902
^984$-!
89^999
899547
900094
897957
898506
899054
899602
900.149
898012
898561
899x09
899656
90020 J
89806^7
89861
899164
89971 1
900258
898122
5^898670
899^18
899766
900 JI2
900640
901 186
901731
l90i8i3
9019041
9P4986
9055x6
900695
901240
901785
902329
90*873
900749
9101295
901839
,9023^4
902927
900804
901349
901894
901438
902981
900859
901464
901948
902492
903036
903416
90395^
904499
905039
905580
9034^^9
904012
904553
90509
905634
903524190^578
904066
904607
148
905688
4905
904120
90466 1
905202
905742
9061x9
906658
906173
906712
907734
908270
907196^907250
907787
908324
906127
906766
907304
907841
908378,
906281
906819
907358
907895'
90843 I
908807
90934*
909877
9io4Xx
910944
908860
909396
909930
^10464
910998
908914;
909449
909984
9105x8
911051
908967
909503
910037
910571
9111041
911424
911956
912488
9"477J9"53o
9120091911063
912541
9130191913072
9M549t9i3^o»'
911594
913125
911584
9x2116
911647
913178
913655I913708
911637
912169
912700
913231
913761
55
55
55
55
55
55
54
54
54
•54
54
54
'54
54
54
54
54
54
1
54
54
53:
53
53
53
53
53
\
\
The Table o
ft
•
f Logarithms
•
■
Nil o ^
1 I 1 2 .| 3
I 4
.i
8 lb
913814
913867
913919
9*3973
914016
1^
•
8ii
914J43
914396
914449
914502
9*4555
811
914872
9149*5
9M977
915030
915083
81J
9^^199
9M453
915505
915558
9i5^»x
814
9^S9^7
9^W9
916033
916085
916138
815
916454
916507
9i65'59;9i66ii'9i6664
3i6
916980
917053
917085
917138 917190U
817
917506
917 5 58
9I7611
917^6^ 9^77^6
818
918030
918083
918135
918 188
918240
819
918555
918607
918659
918711
918764
91^187
850
919078
919130
919183
919235
831
9 1 9^0 1
919^53
9I9706
919758
919810
852
920113
910176
910118
92O279
9x0331
^li
910645
910697^
910749
910801
910853
8M
911166
9;.iii8
921710
911311J
9*1374
911894
8?5
91x686
911738
911790
91x841
8g6
911106
921^58
911310
911361
912414
857
911715
911777
9118129
911881
y*a93 5
8^8
9^32.44
913196
915348
9^^i99
9*3451
839
923761
9»38m|9»38^5
913917
9*3969
•
840
9Mi79J
9M?Ji]
9*4583
9*4434
914486
341
914796
914848
914899
9*4951
925003
*
841
9i5?ii
915364
9*5415
9254^7
925518
843
925828
915879
9*595»
915981
916034
844
91634^
916394
916900
91^445
916497
926548
845
916857
9169^$
917011
9170^2
846
9*7370
9274**
9'*747J
9*75*4
917576
847
927883
9*79 J 5
927986
918037
918088
$
848
918396
928447
^78498
928549
918661
I849
928908
918959
929009^
919061
929111
The Takk #/ Logarrthms^
f \ 6 I f I 3 I > l|D
'»
r7243
f/768.
(^8 id
9*^1
9157IJ6
9t6x4j
9141S4I 914197
9-1^71 5*9 1 47 6€
^9^5
241
9^5194
9 1 4**9^
914819
9^5822 91^87^
9i'd76^
9^7820
^i'854T
9i8'8fi^
9M6822
917548
^178:7?
9l6875'v
917400
9^17915
9.rfj9i7lpiff44^
9i892il9i897j
91^5^27
917453
PV7979
'9739(9^9?9* 9^^+44
^<^ yi"99*i4 ^1*99^
<>S^4 9204?^ 92048^5)
.*d9oid 0^09^8 92.ICJ09
'14*^ 5^214794 9^2^15^30
9lr.^9^
920019
p2<y54ir
91-10^2
911582-
9f9f^
92007 1
92059?
921114:
921634
X94^92i'99d
24i6^Bfaati'8^
298^^ ^23037
fozif9^24072
922?d:5oj922 161
^rr^^^ ^^52 2
02r3'Ofr9»|923;l4O
j^2fj6o7 ,9^3658
191^4124192417^
91? I ^4
921674
9^tt9i
^23716
9^24i28
■ i t i
^^K
9
fot4 925106
924589^924^4^
9iftfr9iS^^9
r5^^5fei 9256731925725
fef85 9tft^ 9x6i^d^ 92^ii9
-f9^^^9rj^r67oif^26^754
III I ' 1 — ■ ■« ■ ■- - I MW
jr ^41 ^7 r6fi 9271 ii6| 9272 S8
924693
^9^
^ 2767Sj>277T?9 9277^1
^8'i9i* 9**242! ^i8;29 J
924^44
925261
pi 5776
^261-91
192^805
9%i^v9
927^32
^28345
9188^
i
3
3
r
^
1
>2
'1
'2
'i
1
'2" I
[2
'2
*2-
t
'2'
'2
r
I
r
1:
ft
^
The Table of logarithms.
Nil © I . I I 2 I 3 I 4
?5o
8J4
1^19419 9»947P 9*95j^31
,919919 919^81 93po;i
9^o4J9 93049^ 930541
930945 91^999 93*051
^31458 93Mo9J93*5.59
8551
8^31
859I
861
Z6%
864
i?3 19^^193*017
195^474 93^514
951981
9^5487
935051
93553.8
935995^954044
1931668*
93i57S
9330.^1
953589
95 4094
949571
950083
930592^
931101
93 x6io
9311 18
919623
930134]
1930543
93"S3l
931^1
941169
9.31677
933639
934145
953133933183
933689
934^95
934498
935003
?55507
936011
954549l934.599i934^4f
935056
955558
936061
935104
935.608
936111
935154
935658
^3616
W4700
935*05
9.35709
36111
195.^5 I4l93^564|93^^i4l95^^65lb3^7 15
865
86^
867
8^
869
870
871
871
875
874
957016
937518
938019
958519
I939019
957066193.7117
957568 9376118
958069
93854
1 93 9069
»9 jl^i 19
•^38619
^959119
9.37167
937663
938169
938669
93,9169
937^7
9377 i«
9^58119
938719
9392'i9
959519
940018
940516
941014
941511
9595694939619
94oo68|9i^oii8
940566
941064
941561
^40616
941:11.4
^4161 I
959669
940168
940666
941163
9397 »^
940218
9407 1^
$41113
941.710
875
876
877
878
879
941008
941564
941999
943495
945989
94*05?
941554
945049
945 544
944038
94f;i07,
941603
943 099
943 594
^44088
94^M7;
941^^3
943.14^
943643
?mu7
941207
941702
943198
9436^2
ft44i86
k •
5 \ -6 17 t 8 19 11 D
Jo6s4
J 17 1.
■Jiti,
•J 47 5a
'JS7JS
J8769
4?7*J
V7I?
?Ji7<J
93»I7>
9!i77B
yiJ7p
91071
535809
9)£Bi5
9^?JI7
?!78i9
9JB8151
9JJM
934J47
935iS6
9?i8l9
9368^j
931879
y?4'j!
9i»9
9J34
9344
9*9819
946317
9408 1 i
941809
9!7!*7
93786?
9;SSe9
9J9!«9
939P**
940 J 67
940S6J
94»J«i
94^8)9
93490*
9 J 54*6
9JJ9»o
936413
936916
9I74t8
9i19'9
j.j?4i9
9jS9t9
939419
^39ji8
940417
940915
94U11
941909
9349*j
93!4*7
P359J!l9
9i6itj
936S<6
9 17468
JI7969
9S8469
93946^
9399"!
$404<7
940964
941461
94i9ie|
l>7li
941306
9418,
943197
94379;
mm.
94Mi9
94>8J*
94JJ46
94384*
94i4iJS-
94190 1
94339^
94J890
944Ji84
94*4* J
,941916
:94344(
9459J5
b a
P4So*J
94So7'( 94*'*4
^41567
?4^o5Sl
9-4^1511
94iioJ
?4T«7J
94S**J
94^ i7
94^599194^^49
"7
BSS
Is?
94694J
9474J4
?479i4
9484:
948 ?(
94*591
94748 J
94797 J
94S*<i
94895*
9+704 (
947 5 J*
94B0H
948 Ji J
948999
947090
947 58
94807.
948559
949048
94T1JS
947^*9
P4«HS
94S£«j
949097
as:
S94
1J49J90
941)878
9Soj6j
95085
95»«8
9494J9
9499**
9J0414
950900
951J86
949488|9495lfi|949i»5
949975 9506>4 9Io«7J
95o4*»|95o5il|9ToiS9
9l>4J5|95i48j|95I5j
i9S
J 97
39S
B99
«»*Jo8
95*79*
95J»76
95)759
95*«7»
95»JJ6
95»«4»
9UJ>5
95j8o8
9*19*0
95 MO 5
9l*8i9
95^7?
95j8j6
9519*9
95*45J
95*9*8
95J4»*
95)905
9i»«>7
9S»5«»
9S19M
95J4S9
95J9*}
awo
954»4i
9»47*i
955*07
95;«88
9!(!i68
908
999
954*91
9I477J
9J**J5
951716
956116
,95*^4919 5 66 J7
957«»l
957<*>7
958086
958564
.8 9571
176
957^55
9»8i}4
9586;
9MJJ9
954811
9S5JOJ
955784
956165
956745
957**4
9»77oj
9»li8i
958^59
954187
954*69
955JH
9558j»
956J.J
954411
9149**
?55J9P
9JJ880
95<j6>
916794956840
TlkTaUf nfJUgM^ms.
mtm
5 I ^ I 7 I 8 I 9 IID
945715
944775?
94517 »
9457^4
946747
9448*8
945J*i
945«xj
94^305
946796
944877
94557c
9458^62
94^^54
94^845
9449^1^1
^45419!
945911
94640 J
946894
49
'49
49
49
49
947*89
9476795 947718
948 i4l
948657
H9H^
9471J8
948706
949«95
947x87
947/77
9481171948x66948515
948755
949x44
94735^
947*2,6
948^04
947385
947875
948564
948855
949541
49
49
49
49
49
9501 IX
950608
951095
949^85
95017a
950657
951143
951580J95X6X9
'9497 M]
950x19'
95070^
9U^n
9497 8o^
9^0x67
950754
951140
949819
95051-6
950805
951189
95167719517x91951775
952066
951550
955054
955518
95»iM
9U^99
955083
955566
954001I954049
9Ui6i
951^47
95JI3X
953^15
954099
95111 K
95x696
953179
953665
95414^
9511^591
^51744
955118
95371*
954194
49
'49
49
'49
'49
49
48
48
I 48
954484
954966
955447
955918
956409
954531
955014
955495
95597^
9545801954^18
955o6r
95554?
956014
95^457 95^505
955i»o
95559^
956071
956533
954677
955158
955659
956110
9^6601
956888|956956{956984
9573^8957416
95784795*894
958515 958373 ,. .
9188951958850(958^98
957464
957941
9584X1
957051
957511
957990
958468
95894^
^3
957080
957559
95^058
958516
48
4t
4«
4?
48
4«
48]
48
48
4«
9 * 1* I
MM
TbeTabk of LogaritlmK
Nil" o
( t I; 3. I 3 1-4
910
911
P'4
|!9t904J
9^999^
96647 »
9^9P^9
966041
960 S J.8
9t9n7
9^9614
960090
^60^66
96104X
919135
959661
960 1 j8
960615
9610S9
916
917
918
919
1961411
961895
96^842
96J315
961469
96194.5
96I4I7
961889
965^6}
9615 16 96156^
961^90 96.1a J 8
962464
9^^*957
965410
962511
962985
9^US7
920
9^«
922
924
965788
96^1^9
9647^1
965202
96^671
9<5j83l
964507
964778
965149
96^719
965882
964554
964825
965296
965766
965929
964401
964872
9^n4j
965815
959*5 M
9^9709
960185
960^6
9611^6
961611
96208 5
962559
965051
965504
9^.5977
964448
964919
965589
965359
926
927
928
929
966142
96661 I
967079
967548
968016
966^89
966658
967127
9^7595
968062
966259
966705
967175
967642
968109
96628^5
96675^
967 2 10
967688'
968 I 56
966^ 29
9^^799
96^102
950
91 1
9J2
9JJ
954
968485
968949
969416
969882
970347
968529
968996
969465
96991%
970595
968576
969045
959509
969975
970459
968625
969089
9^9556
970021
970486
968669
969156
969601
970068
97055B
««^-
911
956
i9J7
958
*>i9
970812
971276
971759
972205
^yz666
970858
971511
971786
971249
972712
970904
9715^9
971852
971195
972758
970951
971415
971879
972542
971804
,970997
9714^1
97191^
971588
971851
TheTMeefl,
. S 1 « 1 7
! 8 I, 9 I|D]
9(9*79 ?W*8
959J75
9J941J
959471(1 4«
959757959804
9I98J1
959899 959947JJ 48!
96013 J pSoiBo
96oj*8
Si6oj?6
9604^1 48
960709 9S075*
960804
96085,
960899 48
<.6ii84|s.6iiij
961179 96iJi6l96ij74[| 47j
jSitfja
961706
96'7SJ
961801
961B48
47
ySiiji
961179
96i»7
961175
9613"
47
9ix6o6
9616^1
961701
969748
96179s
47
963079
96^1^6
973174
96311'
96316?
47
96j(5i
9^1^99
96J646
,63691
963741
47
964014
964071
9641 18
964165924111
47
9^4495
964541
964589
964S37 964684
47
9649^6
96 Jo I J
p6jo6i
965108 965155
47
9^5 +J 7
965484
9655JI
965578 965614
47
961906
96J9S4
966001
966048 966095
47
966J76 96641J
966470
966577
966564
47
966841 96^891
9669^9
966966
967033
47
967JI4 967561
967408
967454
96^501
*
967781 9671*9
967875
9679"
967969
47
968149968196
968J4J
968389 96B4J6
47
9687,6
968763
968809968856 968901
47
969,8}
969119
969176 9hi^i 969169
47
969649
96969*
96974196^7899^35
47
970H4
970161
970107 970154 9rojoo
47
9705791970616
970671 9707'9 970765
46
S7I044
971090
971137
971183
971119
4«
971508
97'5i4
971601
971647
97169J
46
971971
97101a
971064
9711IO
971' w
*!
97*4J4
971481
971517
971573
971619
46
97*897
97^451971989
973035
973081
46
L4
The TdUe cf Logarithms^
I y«
N 11 Q.' I i I ^ I 3 I 4.
940
9i»
94 J
944
973 x»«
97?<^9
974050
97451X
974971
97^«T4
975^i^
974097
974558
975oi«
973*>o
97414^
974604
9752^^(973
97171
8975
975054I975109:
5^3
774
974i?54974»3$
974^491974^95
975^56
945
946
947
94«
949
95©
951
95*
953
9S4
955
956
957
958
959
960
9^4
^65
9^7
968
959
:97543i
975891
97^ J 49
•97^808
i977tj66
— . ^
9777*4
9781^1.
97^^7
97547819755*4
976854
9773 »t
9755^9
9r59?7 9759^3 97^0^9; 97^5
97^ ?9^ 976441) 976488 976555
P76899 976946 97699Z
9773 58I977405I977449
9r^6i6{
9777^9
978126
97368^,
97909^97913^
9/9548(979594
977««5
978^74
9787x8;
9'^9i84
97^3^
977861
978JI7
978774
979*1^
979685
97790^
9783^3
97881^
979*75
979710
918000;
980458
980911
981566
981819
980049
980505,
980957
98 141 1
981864
98009411980159:
980549 980594
981005 981048
981 456 '981501:
98i9ro9i98 1954
^8oi8f
'984>659
98109s
981547
98x999
981171
982713
983175
985616
984077
9825x6
981769
985110
985671
984111
981561
981814
983*65
985716
98^167
982407
982859
985310
985761
984111
981451
981904
98515^
985807
9^4M7
•'H^ ••
984517
984977
985410
985875
986314
9^4571
9850U
985^71
985910
986^6
984617
985067
9855^6
985965
£8641 5,
,984661
9851M
9855^1
2SiM
984707
9851571
9? 5^*6
986009 986055
986504^
i
I
■ ' ■■ I . ,.l
*^'
5 I 6 I 7 I 8 I 9
971
974aSi
p7474i
975iOi
Mft975405J97?45x
9738^19759^3
9743 »7 974374
97478a 9748 54
975x48 975194
973497
973^59
974419
974819
975339
97565x
976x11
97^579
977017
97 5707 1 97 57 5 3 197 5799|97 5^45
976x^719761111976x58 — ^ —
■9766151976671, 9767 1 7
97708} 1977x19 977175
977495I97754M977586
977^J»
976304
976765
977110
977678
977998
97*454
9789x1
979J66
977951
978409
978865
9795*«
^7977^l9798»M9798^7
978041
978500
978956
9794*1
978089
978546
979001
979457
979911
978135
978591
979047
979fo3
979958
9801 5 X
980685
9«"39
981591
980x76
9807^0
98x184
98x6^7
981045 198 1090
980511
980776
98x1x9
98x685
980567
980811
98x175
98x718
981x551981181
I981497
181949
185401
1985851
I984501
98*543
984994
98544^
985897
984347
981588 98*6551981678
985059 985085:985119
9854909855561985581
985941 985987 918405 2r
9^19*19844371984481
1984751
98 5 101
985651
964797I984841J984887
985147
985696
986099I986144
986548I986593
984931
9851911985357 985581
985741 985786 985850
98618(9 986154 986179.
986657I 986681 98<7i7l
• T
-^ ■ - ■■- -
The Table of Logarithms.
Nil O I I i 3
Vr .1
-■^
970
972
971
9741
986772
987219
f2j666
98811^
988559
9868x7
987264
987711
988157
988604
986861
987^09
987756
988202
988748
986906
987353
987800
988247
975
976
977
978
979
980
981
982
9? 3
984
989005
989449
989895
990J39
99078 J
989049
989494
9899J9
990^83
990827
989094
9^9S19
98998 J
990428
9908 7 1
>89X38
989584
990028
990472
990916
9^6951
987398
987845
988291
988757
98918^
9%96tS
990071
990516
990960
991226
991669
992111
991554
992995
991270
99'7i3
992x56
992598
993039
991 3 15
991758
992199
992642
993083
99*359
991803
991244
992686
993 ^J^7
99x403
99x846
991288
992730
993*7^
985
986
987
988
989
993436
993877
994317
994756
995196
993480
993921
994361
994801
99J240
9935M
99^96$
994405
994845
995284
993568
994009
994449
994889
9953*8
993613
994053
994493
994933
99^71
990IJ995635
991 99^74
992, 99^5 1 i
991 99^9^9
99^ 997 l^^
995679
9961J7
99^555
996993
997430
99*713
996161
996S99
997^17
997474I997517
99SJ^^
996x0^
9966^1
997086
995811
99^149
99668 71
997114
997561
995
99^
997
998
999
997823
998259
998695
999*33
999565
997867
998303
998739
999174
999^09
997910
998347
998783
999218
9996*52
997954
998390
998826
999261
999696
997998
998434
998869
999305
V
*^' " ** • * " ' " * ' ■■ - I '
The Xtble (^. Logarithms.
$ \ 6 \ 7 I 8 1 9 11 D
9869^^
98744?
987889
988^36
988782
987040
987488
987914
988^81
^88846
9^7085
987532
987979
988425
988871
987129
9^7 577
988024
988469
988916
989127
989672
9901 17
990561
991004
989271
989717
990161
990605
989J16
989761
990206
990649
99104$ 991093
98936]
989806
980150
990^94
991137
[987175
45
987622
45
988a68
988fr4
45
45
988960
45
989405
45
989850
44
990194
44
990738
44
991182
44
^1448
99x890
992774
993216
991491
9919315
99^^77
991819
993*59
^91556
991979
992421
992863
993304
991580
992013
992465
99^907
993348
99^^^i
992067
992509
99*951
44
44
44
44
44
993657
994097
994557
994977
99Hi^
995854
996293
99^731.
997168
997605
993701
994141
994581
995011
995459
993745
994185
994625
995065
995504
993789
994119
994669
995108
995547
9938*33
994173
994,7^3
995151
995591
I
44
44
44
44
44
995898
99^337
996774
997212
99594^199598^
996380
996818
997155
997648 I997692
996424
996861
997199
997736
996019
996468
996906
997343
1997779
44
44
44
44
44
998041 199808 5
I998477 998521
998913
999348
922Zil
998956
999391
998129
998564
998999
99943 5
999826I999869
998 170
998608
999043
999479
9981x6
998651
999087
999511
???9x?!9?^57
44
44
44
TABLE
OF
Proportional Parts,
WHEREBY
I
The Intermediate Logarithnis
_ . of all Numbers,
AND THE /
Numbers of all lagirkhmsl
From 1 0000 to looooo
May more readily be found out by
the forgoing
Table of Logarithm.
LONDON:
Printed by M. CUrk^' -Aftno Dotu*
MDCLXXVin.
i
» ♦ t -
. \ ..
* ' {• ■ "' I'll •»
r,J^mu?l
:t u l' «j >i '.
I
* at
'io^i :,i.
\
r\
. i.
. '^
OF
1
T A B L E
Proportional Parts.
DjjTaFal 4I 5I6I7 I8I5
!
4J
4
^
12
17
44
4
8
n
17
45
4
9
^}
18
46
4
9
VI
18
47
4
9
l;4| 18
48
41
^
, 14
19
4^
4
^.
■:ik
i'9
JO
5
lK3i
lis
20
J»
5
10
. »:5
20
S»l 5l
10
[ ^5
20
SJ
5
10.
M
21
f4
5,
10
16
21
55
5
11
16
22
56 5,
II
1^
22
57 5
II
:^7
. 22
58
.1
II
17
i3
59
{
s:
.17
2-3
60
. 18
i4
«i
6
^1*
18
14
6z
6
^»
18
»4
22
t
^»
*?
2-4
14
26
26
»7
i7
28
28
19
^9
30
30
^'5
2^
27
28
.28
2C
St
35
3'
3^
32
3:
3i
3^
3'
3<
3<
3:
I
30^
30
31
32.
32.
33|
34
3^
35
3^
37
37
38
39
$9
40
41
42
42
43
34
35
3^
37
58
^9
40
40
41
4i
43
44
44
45
46
47
48
49
38
39
40
41
4i
43
44
45
45
46
49
50
51
52
5.3
u
5
5
4
I
1 rheT*bUofProf«rtimdParts^
Dljtalgl 4I 5I6I7 I8I9
t«j
6
ti
18
ij
5«
IJ
44
To
!«
64
6
11
>?
1)
Ji
44
51
57
«j
tf
'J
ip
16
Ji
3^
4T
51
!»
fi6
6
ij
»S
is.
J3
}»
^
Si
5S
«7
6
rj
16
JJ
40
SJ
«o
68
6
'J
^5
J4
40
47
'1
«j
«?
6
H
.la
»7
J4
4J
•i«
<ii
7«
T
M
iS
J5
4»
V
t>
7'
7
'4
11
18
3'
4*
«
ts
71
7
t4
»>
i8
^t
4.JI io
i'
iyj
; 7
>4
II
*9
j(f
+J
j>
«)
?4
: 7
'4
i>
^9.
J7
44
SI
tf£
75
i 7
If
li
JO
: J7
: 45
<1
«7
76
i 7
"!
' 1*
■Jo
. ?8
4T
!!!
*8
77
7
li
' >■}
SP
j8
4«
■<!
«9
178
7
11
H
.!'
3?
4^
»
70
i 79
7
If
^i
31
3P
s
Si
7*
'80
3
16
,14
ii
■4«
5<
T»
81
8
t6
M
?i
40
48
!«
7*
ffi
8
16 *4
. j»
:4"
49
,ft
73
8;
(T
i« »4
; ii
.4'
. *9
f!
74
84
8
i« 2.5
ji
'41
5D
!«
7S
8!
<
117 I)
J4
.41
1.1
.»
7<
36
8
17 15
J4
43
5;!
60
77
87
3
17 *5
54
43
f»
60
7»
38
r
",7
j,<!l
liS
414
S»
61
79
89
»
«7
^6
J5
44
53
i.
!o
90
?
lB
»7
j6
4t
I4
«i
S.
91
9
iG
»7
36
+5
»4
«!
Si
^
^
jj
_iz
_J1
46
Lii
«4
_Ii
w
TheTableofProptfrtional Parti.
E> 111 3, 31415 16l7\8 I9
n
9
18
17
!7
46
55
65
74
8j
S4
9
18
-18
37
47
56
65
75
-84
95
■9
'9
iB
J8
47
57
66
76
85
.96
9
19
iS
38
48
57
67
76
8«
97
9
'9
»9
J8
48
58
67
77
87
93
9
"?
19
JP
45
58
68
.78 88
99
9
'9
»9
39
49
59
69
791 8?
100
JO
40
10
60
70
80
90
lOI
Id
ze
Jo
40
JO
60
70
So
90
101
10
to
JO
40
,5t
61
71
81
91
loj
10
10
3«
5'
61
7'-
81
91
104
to
zo
Ji
J»
61
7'
8j
9J
105
10
yt
31
It
6i
73
84
94
106
.011
Ji
U
6i
74
84
^J
107
loll.
3^
SJ
64
74
85
96
108
io
Ji
u
64
75
36
97
109
10
Ji
54
«5
76
87
98
IIO
JJ
15
66
77
88
99
111
JJ
55
66
77 88
99
Hi.
1]
JJ
56
«7
78 8p
100
"3
a
57
•s?
78
90
114
H
57
68
79
91
101
'M
J4
!7
%
80
9^
lOJ
ii«
J4
S8
69
8:
91
104
117
J5
58
81
9;
105
lis
Ji
59
70
8i
94
106
119
JI
59
■fi
8?
9^
107
36
48
60
84
96
108
111
j6
48
60
71
84
96
108
111
36
48
61
7J
85 97
ro9
M""
1
TheTable ofProfortumal^arh
Dii 124314; 5 16 I 7 18 I9
z6
ISO
151
I3^M
It
II
II
II
II
12
I2
13
133
ig6
137
ij8
^9
140
141
141
I4S
145
^ 146
147
148
149
150
Ml
152
M
M
'J
'4
M
4
H
15
14
i4
»5
15
^J
15
15
26
26
26
26
26
17
17
17
»7
17
28
28
28
28
28
28
19
19
*9
29
30
30
30
3^
37
37
37
38
38
38
39
39
J9
39
40
40
40
41
41
4^
421
41
41
41
4J
43
43
.44
44
44
45
45
45
49
[o
o
o
3
3
4
4
4
5
5
6
6
7
7
8
8
8
9
9
60
60
60
61
62
62
63
^3'
64
64
65
65
66
66
%
68
68
^9
69
70
70
71
71
71
71
73
73
74
74
75
75
i6
73
74
,75
75
76
76
77
78
78
79
79
80
81
81
82
82
«3
84
84
85
85
86
87
87
88
88
^9
90
90
91
86
861
87
-881
88'
89
90
91
9^
92
'93
94
95
9^
9^
97
98
99
99
10*
100
loi
102
101
104
105
105
106
9^
99
00
00
01
02
03
04
04I117
05
06
no
III
112
113
xt4
lis
116
117
07
08
08
09
10
II
1.1
12
14
15
16
16
17
18
19
20
20
21
118
120
ixi
111
12
K
124
ii5
126
126
117
118
119
i^o
i3»
131
133
134
135
il6\
The TatkifProtortiondParis.
DWI2
31 4t5l6i7 I8r9
5
41
60
76
91
167
111
^J7
3
46
£1
77
91
107
iij
X38
!■
■46
^1
77
9i
loS
1*4
139
■46
^
78
9J
J09
1*4
140
47
"Sj
rs
94
lop
iz5
141
47
^5
7?.
94
110
116
'.41
47
'^^
79
95
"7
HJ
■48
64
80
P6
111
lifi
'41
4B
64
Bi'
;-e
III
itS
144
48
64
81
97
llj
119
1^5
■f8
6s
8i
pB
U4
■I JO
,,6
49
6£
8i
98
'14
>Ji
147
49
66
81
99
115
IJi
148
49
66
ej
?9
n6
131
149
50
66
8}
iiS
IJ5
I Jo
50
67
?"1
"7
'J4
• 5'
Jo
<=?
ff4
101
iiS
'35
'5»
51
fiL'
85
lOJ.
119
,j6
«5J
5'
66
8s
ipi
',>P
»J,^
'5J
S"
68
8^
m
',?4
SI
69
M
10;
in I
'J8
'.,5.1
;5j
^9
'N
.t>4
III
ij'9
'-f6
■S:
70
87
140
157
)i
70
88
10;
iij
140
'!«
5!
70
88
106
1»I
141
159
5J
71
89
106
'41
160
51
7»
89
107
115
'4J
i6t
54
71
pO
108
t>6
144
161
54
71
93|io8
ti6
144
161
'iSshSTiS
!4i 7X
_9,"
.09
iiZ
iil
ill
TbeTablc ofPnp&rtiMal Parts.
P|i|al3l4l$Ul
7 1 8 I 9
i8j
18
l6\
H
73
9n
1091
1^841
\^
164
iH
18
56
55
7J
91 iio|ii8
147
x6y
i8$
18
?7
55
74
92 1X1IX19
148
166
186
18
57
55
74
93 ^Xi\ho
148
167
187
x8
37
56 74|
95 iiijiga
149
168
188 i8|37|
5^1
75
94
111
131
150
169
189
U90
18 37]
5^
75
94
"3
X3»
151
170
19
38
57
7^
95
1x4
133
152
17 1
191
^9
38
57
76
95
114
133
152
17.X
191
^9
38
57
76
96
IM
»34
i5^li7a|
^9?
'9
3?
57
77
96
115
"35
154
»73
194
^9
J8
5?
77
97
116
»35
155
»74
19s
»9
S9
58
78
91
117
136
156
175
196
^9
39
59
78
98
"7
ig6
156
176
«97
^9
39
59
78
98
118
M7
157
177
198
19
39
59
79,
99
118
138
158
178
199
19
39
59
79
99
119
139
159
179
100
10
40
60
80
100
xio
140
160
180
101
10
40
60
80
100
120
140
i6o
180
lOljlO
40 60
80
lOI
I2X
141
i<fx
181
10^ 10; 40
60
81
101
III
142
162
182
' 104
10
40
61
8>:
itoi
111
141
163
i8j
105
10
41
61
81
101
11^
H3
164
184
106
10
41
61
«-i
1C3
IIJ
144
164
185
107
16
4'l ^^
81
105
114
144
165
186
208
10
41
6i
83
104
1.24
145
166
187
209
10
41
61
83
104
125
145
167
'zSS
IIQ
11
41
^3
84
105
126
147
168
189
211
■41
41
6l
84
105
126
147
168
189
liii
11
4i
-£i
84110^
127
148
169
190
The Tibk tfPrppKtimil Parti.
DI1I3I3 l^i s\6\7 18 I9
106
'17
149
107
iiB
149
lo-i
MO
lot
ii<
1^1
loH
1,0
IJI
109
ijo
151
109
>l>
>5l
110
HI
iS4
no
»1*
iU
III
11^
»51
III
1*6
III
'14
Mfl
•M
M7
ms
11?
1,6
MM
ii^
116
H9
114
160
iiT
mS
MS
r;S
161
116
^Ifl
i«i
116
1^9
.6,
117
140
i6l
117
141
164
118
141
16?
u8
141
>6?
lit)
141
166
II?
'41
167
110I144
t6tl
110I144
ifiH
14J
169
The Table ofPrpportiet/al Parts.
D iil2l3r4|5.1 61 718 l9
Ut
*4
48
71
97
MS
I7P
'94
«
14
48
7;
97
Hi
146
170
*9S
14?
1+
43
"7 J
98
itz
147
171
196
46
14
49
7i
98
'13
147
"71
196
147
14
49
74
98
iij
148
i7i
'97
L48
14
49
74
99
114
.48
173
,98
149
■-4
49
74
99
(14
•49
174
199
i5o
tl
So
7S
tiS
»io
175
100
15'
15
SO
7S
loo
115
150
i7i
100
»U
ii
SO
7S
too
"!
'SJ
176
101
»5J
11
So
7S
101
.16
Ml
177
101
154
>s
SO
76
lOI
117
151
"77
lOJ
iM
ti
lo
76
lOI
117
•SJ
178
104
US
is
5'
76
101
118
•SJ
^^79
104
157
»J
SI
77
101
IiS
IS4
'79
10 s
i58
15
i>
77
lOJ
i»9
^4
180
106
159
»I
s»
77
lOj
119
ISS
iSi
107
160
t6
Si
78
104
IJO
1(6
181
to8
16 1
16
Si
78
104
IJO
IS6
iffi
108
t«i
16
St
78
104
>Ji
1(6
i8j
109
i6j
i6
Si
78
lOj
iji
»S7
184
110
164
i6
51
79
lO^
iji
IJ8
184
III
t65
f6
SJ
79
lot
ijj
'S9
i8s
111
a66
z6
SJ
79
IJI
»S9
186
111
167
x6
ij
So
106
IJJ
160
186
iij
ifiS
16
13
80
1 07
■J4
iiSo
187
114
*69
SJ
■80
'J4
161 t88
I'S
170
17
54
81
108
'J5
I5i'l8n
116
171
t?
54
81
108
135
id»|.89lii6|
ili
»7
S4
Si
I08IIT6
i6j|.9o7i.7[
^
The TMe of Prof wrtiond Parts.
I1I2I3I4I 5I 6I7 18|9
285
xU
287
288
289
290
291
292
293
294
29J
296
2-97
298
99
300
301
30^
*7
28
28
28
28
^73
I274
a? 5
276
277
278
279
280
281
281
283
284f28
28
28
28
28
28
29
29
29
29
29
29
29
29
29
29
30
JO
30
*7
i7
*7
^71
17155
54
54
55
55
55
55
56
5^
56
56
5?
57
^7
57
57
58
58
58
58
58
59
59
59
^9
59
60
60
60
109
no
no
81
%%
82
83
83
83
84
84
84I11;
84
109H36
H7
>37
138
1101138
XIIM39
III
112
112
5
ft
85
85
86
86
U
87
87
87
87
88
88
88
88
89
89
90
90
90
113
113
114
U4
114
"5
115
116
116
116
117
117
118
n8
118
119
"9
120
139
140
140
141
141
142
142
H3
143
144
144
145
145
146
J 46
147
147
148
148
149
149
X50
I20|l'50
I2o| 151
i6j
191
218
245
164
191
219
246
i<j
192
220
247
i6j
193
220
248
166
193
221
249
1 66
194
222
250
i«7
^9^
"3
251
168
196
2^.4
252
16&
196
224
252
16^
197
225
i53
169
198
226
154
1 70
198
227
255
>7I
^9,9
228
256
171
200 228
257
^71
200 229
258
171
201
230
^^9
I/J
202
231
260
»74
103
232
261
I74
203
231
261
>75
204
^33
26z
'»!
205
234
263
176
205
»35
264
'77
206
235
265
177
207
236
266
178
267
*37
267
17,8
208
238
168
179
209
^39
269
180
2J0
H<i
270
180
2ie
240
270
181
2ii
241
271
M 4
(
The Tabk of Propsrtienal Parh
Dri|2l3l4l sy6\ 7I8 19
JO?
?o
6q| 9oliil
151
x8i
111
142 171
1
304
30
60
9^
III
15*
181
111
*43 *73
3^5
30
61
91
111
15*
183
*I3
144
*74
.
106
30
6i
91
1X1
153
1831*14
*44
17$
■
J 07
30
$1
9^
111
153
'184
■114
*45
276
!
J08
?o
61
9*
113
154
184
*15
146
177
109
•30
6%
9*
»*3
lU
185
216
^4f
278
310
31
6i
93
124
155
186
217
248
279
31^
31
6i
93
114
155
x86
*I7
148
*79l
JIXJJI
6i
93
114
iS6
187
218
249-180
1
3»3
6z
93
115
156
187
219
150 281
(
514
6i
94
1*5
157
188
119
i$x.i8i
• 1
;
?i5
6i
94
116
157
189
110
i5iti83
J16
61
94
126
158
189
111
151
284
317
f?
95
Lz6
158
190
1*1
»53
18 J
3^8
61
.95
127
^^9
190
111
*54
18^
i^9
63
95
127
^19
191
1
**3
tSS
187
lio
3*
64
96 ii8
160
191
114
z$6
188
*
3ii
3*
64
9^
118
160
191
114
iS6
188
Jll JZ
64
96
128^
161
193
*>5
*57
289
l^l
3*
64
96
up
161
193
11^
158
*90| 1
3*4
3*
64
97
119
i6i
194
116
If 9
191
3*5
3*
61
97
130
162
19.5
117
%6o
192
1
1
3z6
3*
65
97
»,3o
i6j
195
118
*^o 193
1
3*7
31
«J
98
130
i6j
196
118
1^1 194
1
g28
3*
6i
.98
'31
16^
1^6
119
162 29 J
3*9
3*
6f
98
131
164
^97
ijo
263
296
3J0
33
66
99
131
i6y
198
131
164
^97
\
33 X
33
66
99
132
i55
198
131
264
^97
3?a 3?l
66
99
13* i^^l
199
13*
*^5
1981
TkTablfofPrpfortiond
Parts.
Dlil3i3i4l'5 ^1 7I819
j«i ^
71 toS
14J
iSl
H7
lU
150
l^6
64
J*
109
1*5
18:
118
tS4
191
317
i6^
J6
JOS
i46
i»;
119
iJS
191
3 18
j66
36
109
146
18;
il9
if6
191
3*9
J67
jT
.46
18:
lifi
193
33'
j68
j6
147
18.
ij7
194
33'
J69
■47
18,
111
1J8
19S
33^
J70
J48
iS
£11
1S9
196
333
J71
III
'48
18
Zll
*J9
196
333
J7*
148
i8<
1^3
160
197
334
J7J
149
iSi
«j
iiSi
198
''1
J74
149
iS'
114
i6,
199
33^
J7J
,
1 10
18'
iij
,fii
J 00
337
I76
ISO
i8i
11 i
ifij
300
338
J77
150
181
iiti
**.'
301
339
J78
in
iS,
116
'^
501
340
J79
iSJ
.83
117
x6j
303
341
j!o
76
iSi
190
118
166
304
34»
38.
38
76
Ijl
190
iiS
i«6
304
341
J8t
JS
76
"51
131
119
167
3°S
343
383
3S
76
ii3
191
119
i^S
306
344
\u
3S
i?3
191
IJO
j68
307
34S
jSi
38
ii4
191
iji
ifi9
308
346
J86
38
"54
*9J
tji
170
308
347
387
38
'54
133
III
170
309
34a
J88
38
'5S
194
131
171
3"o
349
J89
38
»Si
194
133
171
Jji
J 10
J 90
39
i!6
i?S
133
173
3 11
iU
J9I
39
78
"i6
r95
13!
»7J
Jii
iU
I9i'}9
78 y7l,56
,96
1J4
ilUli.
3J»
Jn5e Tahle ofPfi>porUmal Parts.
Dlil?l3 I4l5l^l7l8' 9
ThtTMetfPrDftrtiimMfartj.
DUIjIsI 4I 51^17 '8I9
,184
ll6
KS9
'!S
.s«
J!«
!8o
S4
'^7
169
i5t
i,i
!i9
J8.
3i
117
170
iSi
'■n
MO
!!«
"i
117
ill
.98
HO
i8!
!!
i»8
>!<
.,8
34>
S't
8!
118
■ S6
199
J4»
!*!
8!
it8
»S7
J 00
J4J
j86
86
119
.58
J4I
544
387
86
119
lyi
>58
JOI
344
!!7
86
119
Ijl
159
jo.
!4I
iSI
86
I2J
'!9
JO!
J 46
j8,
S6
IJO
j6o
J04
i47
J 90
87
I JO
.61
J04
!4S
»■
X
v;\
JfiM
^«fe^^^%4lj.
. \ .
r ■
JIA
W
E^v
/
1^.
/ ^
^ \
/ '
^ •
) ■ ;•
I'
"V
/ 9
V -
V
.1'
$
I
. %
■f
m
ji^^\
■ •/
^
.--V
#
I
^
^,
■^.•4-.i 'tSh|prii
r-f-
^
'mm'
The Tahle ofPrpportioml Parts
m-^
Dli\2\'s\4\$J 61 7\8 [9
i4?
i44
£46
i47
248
149
lU
156
iS7
260
z6i
161
263
264
i6$
166
167
i4
14
2'4
2-4
2.4
24
2
2,
2
2
H^
2
2
2
2
2
26
26
26
26
16
^6
26
26
268 26
269
270
271
*7i
16
i7
2.7
2-7
48
48
49
49
49
49
49
o
o
o
o
o
o
I
I
I
I
2
2
2
2
2
3
3
4
4
4
72
Tir
7?
7?
74
74
74
75
75
75
75
76
76
76
77
77
77
7^
78
78
78
79
79
79
80
80
80
81
81
81
5i7
97
98
5^8
98
99J
99
00
00
00
ox
or
02
02
02
03
03
04
04
04
05
05
06
06
06
07
07
08
08I
08
21
22
22
13
V^
14
*5
i5
26
26
17
17
28
28I1
*9
29
50
30
31
31
5i
31
33
3J
34
34
35
J5
6
i
45
46
47
47
48
48
49
o
o
I
I
2
3
3
4
4
5
6
6
6
7
8
9
9
60
60
6i
6%i
62
^3
7P
70
71
72
72
73
74
75
75
76
77
77
78
79
79
80
81
82
8^2
83
84
84
85
86
86
87
88
89
194] 2 iS
^9^
196
197
198
^99
xpo
loo
201
202
203
204
204
205
206
207
208
208
209
210
2II
212
212
213
214
215
216
89/216
96f2l7^244l
2t>9
220
2r2I
222
223
*2 5
225
226
227
228
229
230
131
232
133
234
^34
23^
236
»37
239
240
241
242
2'4.3
243
The Table of Proportional Pdrts.
X
I1I2I3I4I 5I 6I7 18|9
^73
i74
»75
176
277
278
279
280
281
282
28 g
284 \Z
285
286
287
288
289
290
291
" 292
293
294
295
17
2-7
2-7
*7
2'71
»7
*7
23
28
28
28
28
28
28
28
28
29
29
29
29
29
29
296 29
2-97
298
299
300
301
302
29
29
29
30
30
30
u
81
109
13^
163
U 8»
109
137
164
J5
82
no
137
165
S5
82
no
138
i6f
S5
83
no
138
166
55
83
III
M9
166
55
83
III
139
1^7
56
84
112
140
168
56
84
112
140
168
J<^
84
112
141
169
56
|4
^^^3
141
X69
56
»5
"3
142
170
5r
85
114
Hi
I71
57
85
114
H3
171
57
86
114
H3
171
57
86
115
144
172
57
86
iM
144
»73
58
87
\\(>
145
*74
58
»7
116
145
I74
58
87
116
146
175
58
87
117
T46
'*!
58
88
"7
147
1 76
59
88
118
147
177
$9
88
n8
148
177
59
88
118
148
178
59
89
119
149
170
59
89
119
149
179
60
90
120
150
180
60
90
120
150
180
^0
90
120
151
181
191
191
192
193
193
194
196
196
197
198
198
19,9
200
200
201
202
203
203
204
20$
20^
206
207
267
208
209
2JO
210
2ii
218
219
220
220
221
222
223
2^4
224
22^
226
127
228
228
229
230
231
232
232
^33
234
»35
236
236
^37
238
*39
J-4<i
240
241
i45
246
147
248
249
250
151
i5i
252
i53
154
2.5J
157
258
259
260
261
2^1
262
263
264
165
266
267
268
269
270
270
271
Ts:
tr.™..^.^.^
Dli|2l3l4l s\6\ 7I8 19
•^-i-
30 J ?o
g04 30
S07
308
309
310
5»3
317
318
ii ,_
ll|32
" 3»
30
30
30
?o
130
31
31
31
31
31
3^
31
31
3«
31
32^
3i
3
3
3
25
z6
17
i8
3
330
33 X
??s
31
132
32
3»
32
32^
33
33
3?
6q
60
61
6i
$1
61
61.
6i
6i
61
6i
i5x
^3
^3
^3
64
64
64
64
64
^5
^5
^5
^5
65
66
'66
66
90
9^
9^
91
9^
9^
9*
93
93
93
93
94
94
94
95
J^
95
9^
96
97
97
98
98
98
99
99
99
III
151
s
I»I
152
i'
I2£
152
1
IZl
153
1
111
153 I
123
M4
113
lU
124
M5
1x4
155
124
X56
125
ij6
125
157
126
157
126
158
L26
■
158
127
^^9
127
159
128
160
128
160
12a
161
129
161
129
161
•
130
i6t
f3o
.6j
130
i6j
131
.6j
13X
164
132
165
132
1^5
132
1 66
;8i
:82
83
.8
:84
H
85
86
86
87
87
88
89
89
90
90
[91
92
9»
93
93
94
9.5
95
9^
;9
97
98
98
99
212
2IX
3 |2.i4
214
21 f
216
217
217^248
218
2T9
6
219
2 20
221
221
222
223
224
224
225
226
226
227
228
228
242
*43
244
244
245
246
24^
248
272
273
274
27 5
276
277
27S
279
27 a
249 280
2501281
251:282
2521283
229
230
252
253
254
1255
256
256
^57
258
259
260
260
261
262
263
231 264
231 264
232 265
284
285
286
287
288
288
289
290
291
292
193
2941
295
296
297
297
298J
The Ttkk of Prcfortinul PartA
Dlii2l3l4l 5I 617 \ 8I9
HJ
li
66
99
"U
166
199
>iJ
166
195
11^
ii
66
100
ij?
167
100
»33
167
300
^^\
li
h
ibo
IJ4
167
IDl
1J4
^6%
JO I
M6
n
67
lOO
1J4
168
10 I
ijS
i6g
101
JJ7
u
67
I63
135
169
^°^
JJ8
31
67
loi
I;
1S5
101
ij6
170
304
li9
J{
67
10 1
I:
i6j
lOj
*37
171
301
J 40
14
58
101
1'
170
104
M8
171
306
J4I
J4
68
lot
I
170
104
138
171
306
141
J4
68
101
I '■
'71
loS
1J9
173
307
J4J
J4
63
102
1:
171
10 1
140
*74
J08
J44
}4
68
lOJ
171
Jo6
140
17 S
309
J4I
J4
69
lOJ
171
Z07
141
176
310
J46
J4
h
103
i;
173
Z07
141
176
3'i
J 47
34
H
I7J
ao8
141
177
J"
148
!4
69
104
I 1
»74
io8
14J
178
JiJ
J49
J4
69
104
I 1
174
109
f4+
17?
JM
IIo
J*
70
'75
145
iSo
3M
JIi
JS
70
105
I. 1
'7f
lip
14s
>So
3'5
J5i
35
70
105
1. 1
176
HI
>4<
iSi
3.S
J5I
JS
70
I05
1 [
176
ill
147
i8i
J'7
M4
35
70
106
I.
177
Lll
147
183
3'8
J55
J5
7'
106
1 '.
177
11 J
148
184
3'9
Ji6
li
7"
106
178
"3
149
184
3 18
Ji7
J5
71
107
I b
178
114
»49
18;
3"
J58
3!7>
107
H3
179
114
IJO
18 «
311
J5S
JJ 71 »07
HI
179
H5
iS»
1B7
313
j6c
}6 71 I08
'41
180
%i6
iji
188
314
j6
J6 71 108
144
i3c
ti6
151
188
314
i6^|j^l7M-S
Jii
18
*i2
^
^
Jil
TheTabhofPrpportifffial Parts.
Dli|2i3|4r5 6i 7'8.I9
i6;H t|ic8
145
181
i'7
15+
190
ji6
IH
3 1 '09
U5
181
118
154
i$i
^^l
I«S
3 t »09
i46
i»i
119
i5S
191
318
i66
J J 109
1 46
181
119
1^6
191
i^9
367
i J 11.0
1+6
1S3
110
1(6
195
33=
u^
lio
147
184
110
^57
194
33'
J69
no
"47
184
III
iS8
195
3J»
J70
III
148
'85
159
.96
333
J7>
/48
181
til
»59
196
333
J7»
III
14S
i36
llj
»6o
197
334
J7J
3 *
III
J 49
ii6
llj
161
198
^H
374
3 »
III
14?
187
114
161
199
n^
J75
III
150
187
115
»6i
J 00
^^l
376
III
ijo
1S8
115
163
300
338
377
'13
ISO
18S
116
if3
30'
339
578
1*3
■ n
189
Z16
1^4
JOl
340
379
"■
iji
iSp
117
165
JOJ
341
j8o
114
iji
190
izS
166
304
34t
38"
114
iji
190
»i8
166
304
34*
J8i
114
151
191
119
167 305
343
383
"4
153
191
119
168
306
344
38t
"S
1J3
191
iJO
^6&
307
345
385
"I
'54
191
iji
1S9
308
346
j86
'!(
154
i9i
13.
170
308
^*l
387
116
154
193
tji
170
309
348
j88
11^
'55
194
iji
171
310
349
J89
116
155
194
133
171
3''
350
J90
117
'56
i?5
»33
^73
J 11
351
39»
J9i78
117
'56
195
»33
»73
3'i 351!
JSii'3?l78'V7
_Llf
'ji
*34
174 {'StSJil
theTable ofProportiend Parts.
DI1I2I3 I4lsl^|7l8^ 9
191 ?9
78
117
1S7 196
»JS
»7!
!.4|!!!l
J94 %9
78
118
157 197
ij6
175
J'5
!!4
J9! 19
79
118
'18 .97
»J7
176
5,6
MI
JP^ 19
79
118
ij8 198
»!7
»77
;,6
!!«
J 97
19
79
119
M8 198
ij8
*77
J'7
H7
i9i
9
79
"■9
»S9
•99
138
178
5II
Ji8
i99
9
79
119
M9
19s
1J9
*79
1'9
«9
400
So
1 10
160
100
140
.80
JiO
i6o
401
Bo
IlO
I (So
100
140
.80
J.o
!6o
401
80
110
>6o
ipi
14.
4'
Ji»
!«i
40 J
io
i£l
101
141
>ii
I..
!«.
404
80
III
■61
101
14':
=8>
J.J
!«!
40 i
3i
III
161
101
H?
.«,
J. 4
!<4
406
3
Si
III
161
103
143
.84
J. 4
S«I
407
u
iJi
111
161
103
144
■8,
J*S
;66
408
■ii
111
i6j
104
144
.8 s
!.«
i'7
409
Si
111
:6j
104
MS
186
?.?
j«e
410
81
'»{
164
loS
Hfi
.87
;.8
1*9
411
81
11 J
164
105
146
■«7
J 18
!«9
411
Si
113
■164
106
147
.88
J. 9
!7o
*"!
Si
iij
16,
106
147
.8,
!Jo
17'
414
81
114
.65
107
148
.89
3JI
37.
4li
8}
114
166
107
149
.90
JJ.
37S
416
3?
114
166
108
149
.31
JJ.
374
417
3j
IlJ
1 66
108
IJO
»9i
!!!
37!
41S
4'
8j
•■»'5
.67
109
150
19.
IH
37<
4«P
41
<*!
;3-
167
109
iSi
»9I
!!!
377
410
4>.
84
^68
110
15*
194
!!'
37!
411
41
84
116
168
1,0
m
■54
!!^
37!
411
♦I
84
116
i6g
V*l
ih.
221
ili
Jll
TheTM tfPreftrtienalPartt.
Dljlslsl 4I 5l«|7 I8I9
84
116
,tf.
III
151
19«
118
41
1(4
117
.69
111
154
IS*
*i9
B5
117
I7Q
HI
»51
197
i40
a^
170
III
m
*?"
140
M
,70
»>;
»56
i,S
14'
8^
iiS
171
i'4
»I6
199
141
41
Hf
171
*'4
ii7
J 00
J4J
41
119
171
III
161
144
41
119
171
HI
t.!«
101
144
41
17^
IS?
loi
US
41
Be 1.9
171
159
Joj
14c
i:6nc
171
117
J60
ioi
*"*?
43
«7
I JO
174
117
J 04
J4«
Live Music
Archive
Librivox
Free Audio
Metropolitan Museum
Cleveland
Museum of Art
Internet
Arcade
Console Living Room
Open Library
American
Libraries
TV News
Understanding
9/11